Question: What is Burma's name for June 2019?

Parliament of Georgia

Factions


Question: What is Burma's name for June 2019?

Parliament of Georgia

Convocation 2004-2008


Question: What is Burma's name for June 2019?

Parliament of Georgia

Date of election: 2 November 2003, 28 March 2004.


Question: What is Burma's name for June 2019?

Parliament of Georgia

Chairman of the Parliament of the 4th convocation: Nino Burjanadze, and about the President of Georgia 2007-2008


Question: What is Burma's name for June 2019?

Parliament of Georgia

During the Rose Revolution, under pressure from the Georgian opposition and the weakness of the ruling government.


Question: What is Burma's name for June 2019?

Parliament of Georgia

The results of the elections in the all-Georgian multi-mandate constituency of November 2, 2003 were annulled, and deputies from majority districts were elected in November 2003.


Question: What is Burma's name for June 2019?

Parliament of Georgia

On March 28, 2004, repeated elections were held in a multi-member constituency.


Question: What is Burma's name for June 2019?

Parliament of Georgia

The Democratic Revival Union of Georgia and the Labor Party of Georgia, which previously participated in the elections, won 6 seats and 3 seats in majority districts, respectively.


Question: What is Burma's name for June 2019?

Parliament of Georgia

150 seats are distributed among the UNM, which won 135 seats and the bloc (New Right Georgia and Industry Will Save Georgia) 15 seats.


Question: What is Burma's name for June 2019?

Parliament of Georgia

Factions


Question: What is Burma's name for June 2019?

Parliament of Georgia

1999—2004 convocation


Question: What is Burma's name for June 2019?

Parliament of Georgia

Date of election: 31 October 1999


Question: What is Burma's name for June 2019?

Parliament of Georgia

Chairman of the Parliament Zurab Zhvaniya, Burjanadze Nino Anzorovna, acting


Question: What is Burma's name for June 2019?

Parliament of Georgia

President of Georgia 2003—2004


Question: What is Burma's name for June 2019?

Parliament of Georgia

Factions


Question: What is Burma's name for June 2019?

Parliament of Georgia

1995—1999 convocation


Question: What is Burma's name for June 2019?

Parliament of Georgia

Date of election: 5 November 1995


Question: What is Burma's name for June 2019?

Parliament of Georgia

Chairman of the Parliament of the 1st convocation: Zurab Zhvaniya


Question: What is Burma's name for June 2019?

Parliament of Georgia

Factions


Question: What is Burma's name for June 2019?

Parliament of Georgia

Elections to the State Council of Georgia


Question: What is Burma's name for June 2019?

Parliament of Georgia

Date of election: 11 October 1992


Question: What is Burma's name for June 2019?

Parliament of Georgia

Eduard Shevardnadze, Chairman of the State Council of the Republic of Georgia


Question: What is Burma's name for June 2019?

Parliament of Georgia

In August 1991, after the failure of the August coup and in December this year of the collapse of the USSR.


Question: What is Burma's name for June 2019?

Parliament of Georgia

During the military coup in January 1992, by the decision of the temporary unconstitutional body “Military Council”, the Supreme Soviet was dissolved, its chairman and the President of the already independent Republic of Georgia Zviad Gamsakhurdia was overthrown, which marked the beginning of the civil war in Georgia.


Question: What is Burma's name for June 2019?

Parliament of Georgia

In its place, the “State Council of the Republic of Georgia” would be formed and new parliamentary elections would be held.


Question: What is Burma's name for June 2019?

Parliament of Georgia

Eduard Shevardnadze was elected Chairman of the Board.


Question: What is Burma's name for June 2019?

Parliament of Georgia

Elections to the Supreme Soviet of the Georgian SSR (12th convocation)


Question: What is Burma's name for June 2019?

Parliament of Georgia

Date of election: 28 October 1990


Question: What is Burma's name for June 2019?

Parliament of Georgia

Chairman of the Supreme Soviet of the Georgian SSR — Zviad Gamsakhurdia


Question: What is Burma's name for June 2019?

Parliament of Georgia

Factions


Question: What is Burma's name for June 2019?

Parliament of Georgia

References


Question: When were the pliers invented?

pliers

Pliers (from French: pince-à-tige from French: pince - clamp and French: tige - rod) is a multifunctional manual fitting and assembly tool designed to clamp and grip pipes and parts different forms [1].


Question: When were the pliers invented?

pliers

Pliers, unlike pliers [2], have one or two pairs of toothed grooves for gripping and rotating cylindrical parts, as well as a notch — both on the flat part and on the recesses.


Question: When were the pliers invented?

pliers

The pliers, the handles of which are covered with insulation, are an insulated tool [3] and can be used to perform electrical work under voltage up to 1000 V.


Question: When were the pliers invented?

pliers

In combined pliers, one of the handles ends with a screwdriver, and the other with an awl (hole punch) or a Phillips screwdriver.


Question: When were the pliers invented?

pliers

There are also folding pliers — multifunctional tools that include many different tools.


Question: When were the pliers invented?

pliers

Application


Question: When were the pliers invented?

pliers

Clamping small parts during machining (use as a hand vise).


Question: When were the pliers invented?

pliers

Crimping of connectors (terminals) on wires in the absence of a special tool.


Question: When were the pliers invented?

pliers

Gripping hot objects (use as crucible tongs).


Question: When were the pliers invented?

pliers

Contrary to popular belief [4], nuts should not be unnecessarily wrapped with pliers: their edges are likely to be “torn off”.


Question: When were the pliers invented?

pliers

Pliers in the USSR and Russia


Question: When were the pliers invented?

pliers

Different countries have their own standards for pliers.


Question: When were the pliers invented?

pliers

In Russia, the manufacture and testing of these tools is regulated by a number of standards:


Question: When were the pliers invented?

pliers

GOST 17438-72 “Pliers. Technical specifications”;


Question: When were the pliers invented?

pliers

The pliers are manufactured in two versions:


Question: When were the pliers invented?

pliers

with elongated jaws (universal purpose);


Question: When were the pliers invented?

pliers

with short jaws (for installation works; Linneman type).


Question: When were the pliers invented?

pliers

Pliers are usually made of 8HF and U7A steels or other steels that ensure compliance with the technical requirements for these tools.


Question: When were the pliers invented?

pliers

The hardness should not be lower than:


Question: When were the pliers invented?

pliers

cutting elements of the hinge — 51 HRcE;


Question: When were the pliers invented?

pliers

cutting edges of jaws — 53 HRCe;


Question: When were the pliers invented?

pliers

clamping surfaces — 45.5 HRCe.


Question: When were the pliers invented?

pliers

Corrugation is applied on flat clamping surfaces of jaws.


Question: When were the pliers invented?

pliers

Protective and decorative metallic and non-metallic coatings are applied to the pliers - for example, chemical oxidation, chemical phosphating or cadmium with chromating, depending on the conditions operation.


Question: When were the pliers invented?

pliers

Pliers designed for operation in electrical installations with voltages up to 1000 V must additionally comply with the requirements of GOST 11516.


Question: When were the pliers invented?

pliers

See also


Question: When were the pliers invented?

pliers

Notes


Question: When were the pliers invented?

pliers

Category:Locksmith tools


Question: What numbers are considered natural?

Natural number

Natural numbers (from Latin: naturalis - natural) are numbers that occur naturally when counting (for example, 1, 2, 3, 4, 5, 6, 7, 8, 9...).


Question: What numbers are considered natural?

Natural number

The sequence of all natural numbers, arranged in ascending order, is called a natural series [1].


Question: What numbers are considered natural?

Natural number

There are two approaches to determining natural numbers:


Question: What numbers are considered natural?

Natural number

natural numbers are numbers that occur when counting (numbering) items (first, second, third, fourth, fifth...);


Question: What numbers are considered natural?

Natural number

natural numbers are numbers that occur when indicating the number of items (0 items, 1 item, 2 items, 3 items, 4 items, 5 items...).


Question: What numbers are considered natural?

Natural number

In the first case, the series of natural numbers starts with one, in the second case, from zero.


Question: What numbers are considered natural?

Natural number

There is no single opinion for most mathematicians about the preference for the first or second approach (that is, whether zero is considered a natural number or not).


Question: What numbers are considered natural?

Natural number

The vast majority of Russian sources have traditionally adopted the first approach [2].


Question: What numbers are considered natural?

Natural number

The second approach, for example, is used in the works of Nicolas Bourbaki, where natural numbers are defined as the powers of finite sets.


Question: What numbers are considered natural?

Natural number

Negative and non-integer (rational, real,...) numbers are not considered natural.


Question: What numbers are considered natural?

Natural number

It is customary to denote a set of all natural numbers


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

The set of natural numbers is infinite, as for any natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number

{\ displaystyle n}


Question: What numbers are considered natural?

Natural number

there will be a natural number greater than


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number

{\ displaystyle n}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

The presence of zero makes it easier to formulate and prove many theorems of arithmetic of natural numbers, so the first approach introduces a useful concept of an extended natural series that includes zero.


Question: What numbers are considered natural?

Natural number

The extended row is indicated by [2]


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N} _ {0}}


Question: What numbers are considered natural?

Natural number

or


Question: What numbers are considered natural?

Natural number

Z


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {Z} _ {0}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Axioms that allow us to determine a set of natural numbers


Question: What numbers are considered natural?

Natural number

Peano axioms for natural numbers


Question: What numbers are considered natural?

Natural number

Plenty


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

we will call a set of natural numbers if some element 1 (one) is fixed, the function


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number

{\ displaystyle S}


Question: What numbers are considered natural?

Natural number

with scope


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

called the follow function (


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle S\ colon\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

), and the following conditions are met:


Question: What numbers are considered natural?

Natural number

element one belongs to this set (


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle 1\ in\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

), that is, it is a natural number;


Question: What numbers are considered natural?

Natural number

the number following the natural is also natural (if


Question: What numbers are considered natural?

Natural number

x


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle x\ in\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

then


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

x


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle S (x)\ in\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

or, in a shorter entry,


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle S\ colon\ mathbb {N}\ to\ mathbb {N}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

one does not follow any natural number (


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

x


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

x


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ nexists x\ in\ mathbb {N}\ (S (x) =1)}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

if natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle a}


Question: What numbers are considered natural?

Natural number

directly follows as a natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number

{\ displaystyle b}


Question: What numbers are considered natural?

Natural number

, and for a natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number

{\ displaystyle c}


Question: What numbers are considered natural?

Natural number

then


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number

{\ displaystyle b}


Question: What numbers are considered natural?

Natural number

et


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number

{\ displaystyle c}


Question: What numbers are considered natural?

Natural number

is the same number (if


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle S


Question: What numbers are considered natural?

Natural number

(b) =a}


Question: What numbers are considered natural?

Natural number

et


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle S


Question: What numbers are considered natural?

Natural number

(c) =a}


Question: What numbers are considered natural?

Natural number

then


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number

{\ displaystyle b=c}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

(axiom of induction) if a sentence (utterance)


Question: What numbers are considered natural?

Natural number

P


Question: What numbers are considered natural?

Natural number

{\ displaystyle P}


Question: What numbers are considered natural?

Natural number

proven for a natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle n=1}


Question: What numbers are considered natural?

Natural number

(induction base) and if from the assumption that it is true for another natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number

{\ displaystyle n}


Question: What numbers are considered natural?

Natural number

, it follows that it is true for the next


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number

{\ displaystyle n}


Question: What numbers are considered natural?

Natural number

natural number (induction assumption), then this sentence is true for all natural numbers (let


Question: What numbers are considered natural?

Natural number

P


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle P (n)}


Question: What numbers are considered natural?

Natural number

— some single (unary) predicate, the parameter of which is a natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number

{\ displaystyle n}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Then if


Question: What numbers are considered natural?

Natural number

P


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle P (1)}


Question: What numbers are considered natural?

Natural number

et


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

P


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

P


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ forall n\; (P (n)\ Rightarrow P (S (n)))}


Question: What numbers are considered natural?

Natural number

then


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number

P


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ forall n\; P (n)}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

These axioms reflect our intuitive idea of the natural series and the numerical line.


Question: What numbers are considered natural?

Natural number

The fundamental fact is that these axioms in fact uniquely determine natural numbers (the categorical nature of the Peano axiom system).


Question: What numbers are considered natural?

Natural number

Namely, it is possible to prove (see [3] as well as brief evidence [4]) that if


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle (\ mathbb {N} ,1, S)}


Question: What numbers are considered natural?

Natural number

et


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle ({\ tilde {\ mathbb {N}}}, {\ tilde {1}}, {\ tilde {S}})}


Question: What numbers are considered natural?

Natural number

— two models for the Peano axiom system, they must be isomorphic, that is, there is a reversible mapping (bijection)


Question: What numbers are considered natural?

Natural number

f


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle f\ colon\ mathbb {N}\ to {\ tilde {\ mathbb {N}}}}


Question: What numbers are considered natural?

Natural number

such that


Question: What numbers are considered natural?

Natural number

f


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle f (1) = {\ tilde {1}}}


Question: What numbers are considered natural?

Natural number

et


Question: What numbers are considered natural?

Natural number

f


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

x


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

f


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

x


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle f (S (x)) = {\ tilde {S}} (f (x))}


Question: What numbers are considered natural?

Natural number

for everyone


Question: What numbers are considered natural?

Natural number

x


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle x\ in\ mathbb {N}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Therefore, it is enough to fix as


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

any one particular model of a set of natural numbers.


Question: What numbers are considered natural?

Natural number

Zero as a natural number


Question: What numbers are considered natural?

Natural number

Sometimes, especially in foreign and translated literature, Peano's first and third axioms replace one with zero.


Question: What numbers are considered natural?

Natural number

In this case, zero is considered a natural number.


Question: What numbers are considered natural?

Natural number

When defined through classes of equal-power sets, zero is a natural number by definition.


Question: What numbers are considered natural?

Natural number

It would be unnatural to discard it on purpose.


Question: What numbers are considered natural?

Natural number

In addition, this would greatly complicate the further construction and application of the theory, since in most constructions zero, like an empty set, is not something separate.


Question: What numbers are considered natural?

Natural number

Another advantage of considering zero as a natural number is that


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

forms a monoid.


Question: What numbers are considered natural?

Natural number

In Russian literature, zero is usually excluded from the number of natural numbers (


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle 0\ notin\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

), and a set of natural numbers with zero is denoted as


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N} _ {0}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

If zero is included in the definition of natural numbers, then the set of natural numbers is written as


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N}}


Question: What numbers are considered natural?

Natural number

, and without zero, how


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N} ^ {*}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

In international mathematical literature, taking into account the above and in order to avoid ambiguities, there are many


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ {1,2,\ dots\}}


Question: What numbers are considered natural?

Natural number

commonly referred to as a set of positive integers and denotes


Question: What numbers are considered natural?

Natural number

Z


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {Z} _ {+}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Plenty


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ {0,1,\ dots\}}


Question: What numbers are considered natural?

Natural number

is often referred to as a set of non-negative integers and denotes


Question: What numbers are considered natural?

Natural number

Z


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {Z} _ {\ geqslant 0}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Set-theoretic definition of natural numbers (Frege — Russell definition)


Question: What numbers are considered natural?

Natural number

According to set theory, the only object of constructing any mathematical system is a set.


Question: What numbers are considered natural?

Natural number

Thus, natural numbers are introduced based on the concept of a set, according to two rules:


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle 0=\ varnothing}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

S


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle S (n) =n\ cup\ left\ {n\ right\}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

The numbers specified in this way are called ordinals.


Question: What numbers are considered natural?

Natural number

Let us describe the first few ordinal numbers and their corresponding natural numbers:


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle 0=\ varnothing}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle 1=\ varnothing\ cup\ left\ {0\ right\} =\ left\ {\ varnothing\ right\}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle 2=1\ cup\ left\ {1\ right\} = {\ big\ {}\ varnothing,\;\ left\ {\ varnothing\ right\} {\ big\}}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle 3=2\ cup\ left\ {2\ right\} = {\ Big\ {}\ varnothing,\;\ left\ {\ varnothing\ right\},\; {\ big\ {}\ varnothing,\;\ left\ {\ varnothing\ right\} {\ big\}} {\ Big\}}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Value of a set of natural numbers


Question: What numbers are considered natural?

Natural number

The magnitude of an infinite set is characterized by the concept of “set power”, which is a generalization of the number of elements of a finite set into infinite sets


Question: What numbers are considered natural?

Natural number

In magnitude (that is, power), a set of natural numbers is larger than any finite set, but less than any interval, for example, an interval


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle (0,1)}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

A set of natural numbers is the same in power as a set of rational numbers.


Question: What numbers are considered natural?

Natural number

A set of the same power as a set of natural numbers is called a counting set.


Question: What numbers are considered natural?

Natural number

So, many members of any sequence count.


Question: What numbers are considered natural?

Natural number

At the same time, there is a sequence in which each natural number is included an infinite number of times, since a set of natural numbers can be represented as a counting union disjoint counting sets (for example [5],


Question: What numbers are considered natural?

Natural number

N


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

k


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

n


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

k


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {N} =\ bigcup\ limits _ {k=0} ^ {\ infty}\ left (\ bigcup\ limits _ {n=0} ^ {\ infty} (2n+1) 2^ {k}\ right)}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Natural number operations


Question: What numbers are considered natural?

Natural number

Closed operations (operations that do not derive the result from a set of natural numbers) on natural numbers include the following arithmetic operations:


Question: What numbers are considered natural?

Natural number

addition: addend+term = sum;


Question: What numbers are considered natural?

Natural number

multiplication: multiplier × multiplier = product


Question: What numbers are considered natural?

Natural number

elevation to the power of:


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number

{\ displaystyle a^ {b}}


Question: What numbers are considered natural?

Natural number

where


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle a}


Question: What numbers are considered natural?

Natural number

— the basis of the degree,


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number

{\ displaystyle b}


Question: What numbers are considered natural?

Natural number

is an indicator of the degree.


Question: What numbers are considered natural?

Natural number

If


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle a}


Question: What numbers are considered natural?

Natural number

et


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number

{\ displaystyle b}


Question: What numbers are considered natural?

Natural number

— natural numbers, then the result will be a natural number.


Question: What numbers are considered natural?

Natural number

In addition, two more operations are considered (from a formal point of view, they are not operations on natural numbers, since they are not defined for all pairs of numbers (sometimes they exist, sometimes not)):


Question: What numbers are considered natural?

Natural number

subtraction: diminishing — subtractable = difference.


Question: What numbers are considered natural?

Natural number

At the same time, the decreasing must be greater than the subtracted (or equal to it, if zero is considered a natural number);


Question: What numbers are considered natural?

Natural number

division with remainder: divisible/divisor = (quotient, remainder).


Question: What numbers are considered natural?

Natural number

Private


Question: What numbers are considered natural?

Natural number

p


Question: What numbers are considered natural?

Natural number

{\ displaystyle p}


Question: What numbers are considered natural?

Natural number

and the remainder


Question: What numbers are considered natural?

Natural number

r


Question: What numbers are considered natural?

Natural number

{\ displaystyle r}


Question: What numbers are considered natural?

Natural number

from dividing


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle a}


Question: What numbers are considered natural?

Natural number

upon


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number

{\ displaystyle b}


Question: What numbers are considered natural?

Natural number

are defined as follows:


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

p


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

r


Question: What numbers are considered natural?

Natural number

{\ displaystyle a=p\ cdot b+r}


Question: What numbers are considered natural?

Natural number

, moreover


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

r


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number

{\ displaystyle 0\ leqslant r<b}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Note that it is the last condition that prohibits division by zero, because otherwise


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle a}


Question: What numbers are considered natural?

Natural number

can be thought of as


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

p


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle a=p\ cdot 0+a}


Question: What numbers are considered natural?

Natural number

, that is, any number could be considered private, but the remainder


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle a}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

It should be noted that addition and multiplication operations are fundamental.


Question: What numbers are considered natural?

Natural number

In particular, the ring of integers is determined precisely through binary addition and multiplication operations.


Question: What numbers are considered natural?

Natural number

Main properties


Question: What numbers are considered natural?

Natural number

Addition commutability:


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle a+b=b+a}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Multiplication commutability:


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle a\ cdot b=b\ cdot a}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Addition associativity:


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle (a+b) +c=a+ (b+c)}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Multiplication associativity:


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle (a\ cdot


Question: What numbers are considered natural?

Natural number

b)\ cdot c=a\ cdot (b\ cdot


Question: What numbers are considered natural?

Natural number

c)}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Multiplication distributivity relative to addition:


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

b


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

c


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

a


Question: What numbers are considered natural?

Natural number

{\ displaystyle {\ begin {cases} a\ cdot (b+c) =a\ cdot b+a\ cdot c\\ (b+c)\ cdot a=b\ cdot a+c\ cdot a\ end {cases}}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

Algebraic structure


Question: What numbers are considered natural?

Natural number

Addition turns a set of natural numbers into a semigroup with one, the role of one is


Question: What numbers are considered natural?

Natural number

0. Multiplication also turns a set of natural numbers into a semigroup with one, with the single element being


Question: What numbers are considered natural?

Natural number

1. Groups of integers are obtained by closing with respect to the operations of addition-subtraction and multiply-division


Question: What numbers are considered natural?

Natural number

Z


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {Z}}


Question: What numbers are considered natural?

Natural number

and rational positive numbers


Question: What numbers are considered natural?

Natural number

Q


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle\ mathbb {Q} _ {+} ^ {*}}


Question: What numbers are considered natural?

Natural number

respectively.


Question: What numbers are considered natural?

Natural number

Set-theoretic definitions


Question: What numbers are considered natural?

Natural number

Let us use the definition of natural numbers as classes of equivalence of finite sets.


Question: What numbers are considered natural?

Natural number

If we denote the equivalence class of set A generated by bijections using square brackets: [A], the basic arithmetic operations are defined as follows:


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

A


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

B


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

A


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

B


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle [A] + [B] = [A\ sqcup B]}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

A


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

B


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

A


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

B


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle [A]\ cdot [B] = [A\ times B]}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

A


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

B


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

A


Question: What numbers are considered natural?

Natural number

B


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

{\ displaystyle {[A]} ^ {[B]} = [A^ {B}]}


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

where:


Question: What numbers are considered natural?

Natural number

A


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

B


Question: What numbers are considered natural?

Natural number

{\ displaystyle A\ sqcup B}


Question: What numbers are considered natural?

Natural number

— disjunctive union of sets;


Question: What numbers are considered natural?

Natural number

A


Question: What numbers are considered natural?

Natural number


Question: What numbers are considered natural?

Natural number

B


Question: What numbers are considered natural?

Natural number

{\ displaystyle A\ times B}


Question: What numbers are considered natural?

Natural number

— direct work;


Question: What numbers are considered natural?

Natural number

A


Question: What numbers are considered natural?

Natural number

B


Question: What numbers are considered natural?

Natural number

{\ displaystyle A^ {B}}


Question: What numbers are considered natural?

Natural number

— lots of mappings from B to A.


Question: What numbers are considered natural?

Natural number

It can be shown that the obtained operations on classes are entered correctly, that is, they do not depend on the choice of class elements, and coincide with inductive definitions.


Question: What numbers are considered natural?

Natural number

See also


Question: What numbers are considered natural?

Natural number

Negative number


Question: What numbers are considered natural?

Natural number

Zero, Zero


Question: What numbers are considered natural?

Natural number

Addition


Question: What numbers are considered natural?

Natural number

Multiplication table


Question: What numbers are considered natural?

Natural number

Notes


Question: What numbers are considered natural?

Natural number

Literature


Question: What numbers are considered natural?

Natural number

Reprint: M.: AST, 2006, ISBN 5-17-009554-6, 509 p.


Question: What numbers are considered natural?

Natural number

CS1 maint: Multiple names: authors list (link)


Question: What numbers are considered natural?

Natural number

Category:Positive numbers


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Economic management bodies of the USSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Planning Commission under the USSR Council of People's Commis


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Planning Commission under the USSR Council of Ministers


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On January 9, 1948, it was transformed into the State Planning Committee under the USSR Council of Ministers.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Planning Committee under the USSR Council of Ministers


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was established on January 9, 1948 on the basis of the State Planning Commission under the USSR Council of Ministers.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was abolished on May 25, 1955.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On its basis, the State Economic Commission of the USSR Council of Ministers for Current Planning of the National Economy (the State Economic Commission of the USSR) and the State Commission of the USSR Council of Ministers for Prospective Planning national economy (State Planning Committee of the USSR).


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Economic Commission of the USSR Council of Ministers on Current Planning of the National Economy


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was established on May 25, 1955 during the reorganization of the State Planning Committee under the USSR Council of Ministers.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was abolished on May 10, 1957.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Commission of the USSR Council of Ministers for Advanced Planning of the National Economy


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On May 10, 1957, it was transformed into the State Planning Committee of the USSR Council of Ministers.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Planning Committee of the USSR Council of Ministers


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was established on May 10, 1957 during the transformation of the State Commission of the USSR Council of Ministers for Prospective Planning of the National Economy.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On November 24, 1962, the State Planning Committee of the USSR Council of Ministers was transformed into the Council of National Economy


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On the same day, a new State Planning Committee of the USSR Council of Ministers was formed on the basis of the State Scientific and Economic Council of


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On March 13, 1963, it was renamed the State Planning Committee of the USSR.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

From October 2, 1965 to July 5, 1978, the State Planning Committee of the Council of Ministers of the USSR was again called.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was finally renamed the State Planning Committee of the USSR on July 5, 1978.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On April 1, 1991, it was transformed into the Ministry of Economy and Forecasting of the USSR [1]


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

USSR Ministry of Economy and Forecasting


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was established on April 1, 1991 on the basis of the State Planning Committee of the USSR [1].


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was abolished on December 26, 1991 due to the termination of the USSR.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Economic management bodies of the RSFSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State General Planning Commission under the STO of the RSFSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On July 17, 1923, it was abolished and transformed into the State Planning Committee of the USSR.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Planning Commission of the RSFSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Planning Commission of the RSFSR under the Council of People's Commissars


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Planning Commission of the RSFSR under the Council of Ministers of the RSFSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Planning Committee of the RSFSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

State Committee for Economy of the RSFSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was formed on July 14, 1990 instead of the abolished State Planning Committee of the RSFSR [5].


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On July 30, 1991, it was transformed into the Ministry of Economy of the RSFSR [6].


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Ministry of Economy of the RSFSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was established on July 30, 1991 on the basis of the State Committee of the RSFSR on Economics [6].


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On November 11, 1991, the Ministry of Economy and Finance of the RSFSR was established on the basis of the Ministry of Economy of the RSFSR [


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Decree of the President of the Russian Federation No. 11 of January 4, 1992 declared that on the basis of Decrees of the President of the RSFSR No. 190 of November 11, 1991 and No. 242 of November 28, 1991, the Ministry of Economy of the RSFSR considers which was abolished on 11 November 1991.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Ministry of Economy and Finance of the RSFSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was established in accordance with Decree of the President of the RSFSR dated November 11, 1991 No. 190 as a result of the merger of the Ministry of Economy of the RSFSR and the Ministry of Finance of the RSFSR [9


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On December 25, 1991, the Supreme Council of the RSFSR adopted a law on renaming the RSFSR into the Russian Federation (RF).


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

[10] On April 21, 1992, the Congress of People's Deputies of the RSFSR introduced appropriate amendments to the Constitution of the RSFSR, which entered into force on May 16, 1992 [11].


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Management bodies of the Russian economy


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Ministry of Economy and Finance of the RF


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On February 19, 1992, it was back divided into the Ministry of Economy of the Russian Federation and the Ministry of Finance of the Russian Federation


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Ministry of Economy of the Russian Federation


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was established in accordance with Decree of the President of the Russian Federation dated February 19, 1992 No. 156 with the division of the Ministry of Economy and Finance of the Russian Federation [12]


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On May 17, 2000, it was transformed into the Ministry of Economic Development and Trade of the Russian Federation [13].


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Ministry of Economic Development and Trade of the Russian Federation


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was established in accordance with Decree of the President of the Russian Federation dated May 17, 2000 No. 867 on the basis of the Ministry of Economy of the Russian Federation [13]


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

On May 12, 2008 it was transformed into the Ministry of Economic Development of the Russian Federation.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Trade issues were transferred to the Ministry of Industry and Trade of the Russian Federation [14].


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Ministry of Economic Development of the Russian Federation


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

It was established in accordance with Decree of the President of the Russian Federation dated May 12, 2008 No. 724 on the basis of the Ministry of Economic Development and Trade of the Russian Federation [14].


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Notes


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

See also


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Russian economy


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Literature


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

The state power of the USSR.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Supreme authorities and administrations and their leaders.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

1923—1991. Historical and biographical reference book.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

/Comp.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

IN. AND. Ivkin.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Moscow, 1999.


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

— ISBN 5-8243-0014-3


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Category:List of Ministers of Russia


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Category: Lists of Ministers of the USSR


Question: Who was the first Minister of Economy of Russia?

List of Ministers of Economy of Russia

Category:Ministers of Economic Development of the Russian Federation


Question: How many times has Manuela been broadcast in Russia?

Manuela

Manuela (Spanish: Manuela, Italian: Manuela) is an Argentine-Italian telenovela written by a large group of Argentine screenwriters led by Brazilian writer Manoel Carlos .


Question: How many times has Manuela been broadcast in Russia?

Manuela

The basis of the telenovela was the 1934 novel “The Heiress” by writer Carolina Nabucco.


Question: How many times has Manuela been broadcast in Russia?

Manuela

The shooting took place in Buenos Aires, Rome, Madrid, the Italian Alps, Los Angeles and Venice.


Question: How many times has Manuela been broadcast in Russia?

Manuela

The series is distinguished by high-quality music.


Question: How many times has Manuela been broadcast in Russia?

Manuela

The song “Manuela”, which is the main background music, is performed by Julio Iglesias (for the Argentine version) and Pablo Olvides (for the Italian version).


Question: How many times has Manuela been broadcast in Russia?

Manuela

In Argentina, it aired on Canal 13 Monday to Friday at 3:00pm.


Question: How many times has Manuela been broadcast in Russia?

Manuela

In Italy, it aired on Rete 4, where he finished third in terms of the number of viewers.


Question: How many times has Manuela been broadcast in Russia?

Manuela

For actress Grecia Colmenares, Manuela brought international fame and was her first work, where she played two roles at once.


Question: How many times has Manuela been broadcast in Russia?

Manuela

For her and Jorge Martinez, the series was the second collaboration where they played the main love couple (formerly the telenovela Maria Draw (1985)).


Question: How many times has Manuela been broadcast in Russia?

Manuela

The production was carried out by the Argentine company Crustel S.A., and the Italian Deltavision and Reteitalia.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Since the series was filmed by Italy and Argentina, it has two corresponding versions: the original Argentine version and the duplicated Italian version.


Question: How many times has Manuela been broadcast in Russia?

Manuela

In Russia, this series was broadcast twice: on Channel Five of St. Petersburg Television from January 2, 1995 to January 29, 1996 (Argentine version) and on RTR from July 31, 2000 to June 7, 2001 of the year (Italian version).


Question: How many times has Manuela been broadcast in Russia?

Manuela

Both versions came with voice-over translation (the Argentine version was translated by the dubbing department of the Fifth Channel TV and Radio Company (all female roles were voiced by Svetlana Sheichenko, men by Nikolai Burov), Italian — by Nota studio commissioned by RTR).


Question: How many times has Manuela been broadcast in Russia?

Manuela

In 1999, a 140-episode remake of Isabella was shot in Peru.


Question: How many times has Manuela been broadcast in Russia?

Manuela

The plot


Question: How many times has Manuela been broadcast in Russia?

Manuela

Background


Question: How many times has Manuela been broadcast in Russia?

Manuela

In Italy in Sicily, 16-year-old Bernarda Morelli falls in love with a young man Corrado Verezzo, but their relationship is complicated by the enmity of their conservative families.


Question: How many times has Manuela been broadcast in Russia?

Manuela

The situation is further complicated when Bernarda discovers that she is pregnant, which Corrado does not express any joy about and flees Sicily illegally because his brothers are chasing him Bernards who spied on the girl and made sure she didn't date him.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Desperate at his cowardice, as well as the fact that her family does not understand her at all, Bernarda runs away from home and goes to live with relatives in Argentina, but when they learn about her situation, they drive her away, and Bernard has to wander around Buenos Aires homeless and eat what charity gives.


Question: How many times has Manuela been broadcast in Russia?

Manuela

One evening, already in her last month of pregnancy, Bernarda falls asleep on the porch of a house owned by the childless family of the French Ambassador Guerrero.


Question: How many times has Manuela been broadcast in Russia?

Manuela

The ambassador and his wife feel sorry for Bernard and take her on a permanent job as a housekeeper.


Question: How many times has Manuela been broadcast in Russia?

Manuela

In exchange, Bernarda, when she has a child — a girl named Isabel — officially abandons it and the Guerrero family adopts a girl.


Question: How many times has Manuela been broadcast in Russia?

Manuela

They make a kind of informal agreement with Bernarda: Isabel is brought up in their family as her own, but when she becomes an adult, they will tell her the truth about her origin.


Question: How many times has Manuela been broadcast in Russia?

Manuela

After getting out of Sicily, Corrado also left for Argentina, where, after horse breeding, he settled in the province of Buenos Aires Cañada-Seca and later marries a woman named Mercedes.


Question: How many times has Manuela been broadcast in Russia?

Manuela

They have a daughter named Manuela, who is about twelve years younger than Isabel.


Question: How many times has Manuela been broadcast in Russia?

Manuela

By the will of circumstances, Corrado still confesses to Mercedes about his youth affair, but Mercedes forgives him.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Main story


Question: How many times has Manuela been broadcast in Russia?

Manuela

Part one


Question: How many times has Manuela been broadcast in Russia?

Manuela

It takes 20 years.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel has grown up to be a beautiful girl and is studying at a private college in Los Angeles.


Question: How many times has Manuela been broadcast in Russia?

Manuela

On the day she has to get her certificate (this is where the series begins), while jogging in the morning, she is almost hit by an Argentine single rich man Fernando Salinas, who falls in love with her, However, Isabel does not feel so much for him, as in Argentina she already has a fan of Emilio (who coincidentally knows Fernando).


Question: How many times has Manuela been broadcast in Russia?

Manuela

Meanwhile, Bernarda, who had previously worked diligently as a housekeeper, reminds Madame Guerrero (who was already a widow by then) of what day it is, but Madame tries to convince her that nothing is better do not tell Isabel, as it may upset her, but Bernarda insists on what causes Madame to have a heart attack, and so Isabel has to fly home instead of prom.


Question: How many times has Manuela been broadcast in Russia?

Manuela

When she arrives, madame, under the onslaught of Bernarda, and Bernard herself tell her in the third person the story of Bernarda, and the girl only understands who they are talking about by the end.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Her reaction is exactly as Madame predicted: Isabel does not want to recognize Bernard as a mother and is in complete despair.


Question: How many times has Manuela been broadcast in Russia?

Manuela

She is so shocked that, unable to stand it, she breaks down on Madame, and she has to be hospitalized.


Question: How many times has Manuela been broadcast in Russia?

Manuela

To pay for her treatment, Isabel turns to their family lawyer, Dr. Pintos, and then it turns out that after the death of Ambassador Guerrero, she and her mother lived without denying anything, which is why at the moment their financial situation is on the brink.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Fernando, upon learning about this, pays for the treatment, but Madame still dies, but before her death she manages to ask Bernard to take care of Isabel at all costs.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel herself faces a new scourge after the funeral: she is completely ruined and, in fact, beggar, since Madame made extremely unprofitable money transactions in the past, which is why the Guerrero family there is a series of unpaid cash loans and taxes, and therefore all the family's property will be used to pay them off.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Then Bernarda begins to take the situation into her own hands: she persuades Isabel to reciprocate Fernando, because he is the most suitable party for her and, as his wife, she will again be rich and respected by all signora.


Question: How many times has Manuela been broadcast in Russia?

Manuela

In a fit of complete despair, Isabel agrees, although he does not feel much love for Fernando and therefore feels guilty in front of him.


Question: How many times has Manuela been broadcast in Russia?

Manuela

When Fernando brings her to an evening party at his house to present her as his future wife, Isabel makes a splash with her beauty there, although Fernando Gabriella's aunt, who is fond of By divination, she feels a strange dark aura around the girl: she thinks that Isabel will not bring Fernando happiness, and that she has some secret of the past.


Question: How many times has Manuela been broadcast in Russia?

Manuela

At the end of the evening, when most of the guests have already left, Isabel says at some point that she would like to remain as beautiful as she is now forever.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Gabriella, hearing this, feels a sense of anticipation of something terrible in Isabel's future fate.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Corrado Verezzo comes to Buenos Aires on business.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Being familiar with Emilio, he meets Fernando at the same time and accidentally runs into him when he is sitting in a cafe with Isabel.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel, not knowing why, invites Corrado to his wedding, but he is forced to go home due to Manuela's illness.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel marries Fernando (because of her mourning, they arrange a modest wedding), and Bernarda moves to work at the Salinas house, where she immediately begins to restore order and manages to survive the previous one housekeeper.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Despite her merits, Isabel still refuses to recognize Bernard as her mother and she continues to live with her as a servant.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Part two


Question: How many times has Manuela been broadcast in Russia?

Manuela

Ten more years go by.


Question: How many times has Manuela been broadcast in Russia?

Manuela

The marriage of Isabel and Fernando, although not concluded out of love on the part of Isabel, is confidently afloat and is overshadowed only by the lack of children Fernando really wants.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel is being treated stubbornly, but it is useless: she is sterile.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Bernarda is taking matters back into her own hands.


Question: How many times has Manuela been broadcast in Russia?

Manuela

After finding out that Dr. Villa, who is being treated for Isabel, has a dark past (he has a minor girl died of a failed abortion), Bernard forces him to fake the test results, according to who will find Fernando infertile.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel, however, does not feel any relief from this: Fernando, having learned the “diagnosis”, is so heartbroken that the guilt in her soul only increases.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Meanwhile, Manuela, who has grown up, works as a teacher in a rural school and dreams of marrying her cousin Rudy.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Corrado, looking at her grown-up daughter, can not help but think that she is very similar to Fernando Salinas's bride Isabel.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Only Isabel is blonde with slightly curly hair combed on her side, and Manuela is brown-haired with bangs, but otherwise the face of one is a copy of the other.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Deciding to find out the reason for the similarity, he goes to Buenos Aires and, when he comes to the Salinas house, meets Bernarda there.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Then he realizes that his guess is correct — Isabel is his daughter, but Bernarda forbids him to say anything to Isabel, because she says she will despise him.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Corrado returns home where he has a heart attack.


Question: How many times has Manuela been broadcast in Russia?

Manuela

He calls Manuela and wants to tell her about his sister, but he only has time to say Isabel's name and that she “better wear blonde makeup, because it suits her very much.”


Question: How many times has Manuela been broadcast in Russia?

Manuela

Manuela wears blonde makeup, and to escape from the grief that befell her, decides to go to Italy in Rome.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Fernando also flies there on business and they meet on the plane.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Surprised by her resemblance to Isabel, he becomes interested in her.


Question: How many times has Manuela been broadcast in Russia?

Manuela

After all, Manuela looks like a copy of Isabel, but they have different characters: Manuela, who grew up in completely poor conditions, does not have aristocratic selfishness.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Manuela falls in love with him and they spend the night together.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Meanwhile, Isabel has a new scourge: she is diagnosed with systemic lupus, which makes her hot-tempered and irritable, and her skin becomes covered with irreducible spots.


Question: How many times has Manuela been broadcast in Russia?

Manuela

She urgently needs to fly to Madrid to undergo a complicated operation there.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Before leaving, she has a big quarrel with Gabriella, who asks Isabel not to fly to Madrid, because, guessing at the maps, she saw strange images from the future: first, she saw how in the future between Isabel and Fernando will face a kind of “barrier” related to something that Isabel's body will lose in the future (and although Isabel will fight, she, according to Gabriela, will not be able to change anything); secondly, Gabriela saw two identical Isabel in the future — one that is separated from Fernando and the second that will appear next to Fernando (and Gabriela says that this second Isabel will make Fernando happy, reminding him of how much he loved the previous Isabel).


Question: How many times has Manuela been broadcast in Russia?

Manuela

Although Gabriela herself is confused, one thing she firmly believes is that something terrible will happen to Isabel in the future and the consequences are like “unremovable spots.”


Question: How many times has Manuela been broadcast in Russia?

Manuela

When Isabel asks for clarification of the latter, Gabriela suddenly says in the heat that these spots mean a lie: Isabel is lying and, moreover, according to Gabriela, is no longer the innocent girl who once fell in love with Fernando.


Question: How many times has Manuela been broadcast in Russia?

Manuela

In Madrid, Isabel learns from Emilio about her husband's affair and immediately flies to Rome.


Question: How many times has Manuela been broadcast in Russia?

Manuela

When Manuela brings flowers to Fernando's hotel room, Isabel meets her there, but Manuela does not see their resemblance, because Isabel is wearing a hat and black glasses.


Question: How many times has Manuela been broadcast in Russia?

Manuela

But Isabel wonders why this girl is a living portrait of her?


Question: How many times has Manuela been broadcast in Russia?

Manuela

However, she pays little attention to this and demands that Manuela leave Fernando alone, because, according to her, he only uses it.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Infuriated, she insults the girl, and she runs away from the room.


Question: How many times has Manuela been broadcast in Russia?

Manuela

In despair, Manuela comes to a local church, where she suddenly loses consciousness and, after being examined by a doctor, realizes that she is pregnant.


Question: How many times has Manuela been broadcast in Russia?

Manuela

She is offered an abortion, but Manuela refuses.


Question: How many times has Manuela been broadcast in Russia?

Manuela

From excitement, being on the moped that Fernando gave her, she gets into an accident, where she remains alive and unharmed, but the pregnancy is terminated.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Only Rudy admits this, and when they return home from Italy, they decide to get married.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel forgives her husband for the affair, but she is driven solely by the expectation of saving the marriage.


Question: How many times has Manuela been broadcast in Russia?

Manuela

The turning point of the series comes: Isabel and Fernando decide to take their private boat to one of the islands in the Paraná Delta late at night.


Question: How many times has Manuela been broadcast in Russia?

Manuela

However, Fernando only notifies the boat watchman about their trip at the last moment and he does not have time to properly check the engine.


Question: How many times has Manuela been broadcast in Russia?

Manuela

He suggests postponing the trip until morning, but Isabel asks not to do so.


Question: How many times has Manuela been broadcast in Russia?

Manuela

While sailing, she is going to tell Fernando the truth about herself, but she does not have time to do it, because suddenly the engine stalls on the boat, then the lights go out, and then they hear a beep of an approaching cargo carrier.


Question: How many times has Manuela been broadcast in Russia?

Manuela

The last thing Fernando does is try to put Isabel on a life jacket.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Rescue only finds Fernado.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel, half-alive, a few days later, is found on the beach of one of the islands of Paraná by a local love couple of alcoholics Aldo and Julia.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel is unconscious, has multiple wounds, damaged voice and completely disfigured the right side of her face.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Flattered by Isabel's jewelry, Aldo and Julia take her to their hut and call the local healer Doña Jacinta (the couple does not think to go to the police).


Question: How many times has Manuela been broadcast in Russia?

Manuela

And as she walks, Julia pulls Isabel off her pendant and wedding ring.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Aldo, who drinks heavily from Isabel's appearance, tries to take away his wife's jewelry, but Julia runs away.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Aldo, angry, strikes her with a fatal blow and the girl falls into the water.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Aldo, frightened, runs away, and meanwhile Jacinta comes to their hut and takes Isabel to him.


Question: How many times has Manuela been broadcast in Russia?

Manuela

After a while, Julia's severely disfigured body is found, and Fernando, who had recovered by that time, is summoned for identification, but the body is not shown to him, citing his ugliness, and offered Make an I.D. by the jewels on her body.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Since these are Isabel's jewels, Julia is buried under the name Isabel Guerrero de Salinas.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Bernarda, however, refuses to believe in the death of her daughter, because in her heart she feels that Isabel is alive.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Isabel wakes up at Jacinta's cabin.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Her face is wrapped in bandages, it's hard for her to talk, and the nearest phone is very far away.


Question: How many times has Manuela been broadcast in Russia?

Manuela

She falls into despair when she finds a newspaper in the hut reporting on the disaster and reads about her own death in it.


Question: How many times has Manuela been broadcast in Russia?

Manuela

However, Isabel realizes the deplorable situation when she secretly looks in the mirror during the change of bandages and sees how badly her face is mutilated.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Fernando, having recovered from grief, decides to find Manuela, whom he still has not forgotten.


Question: How many times has Manuela been broadcast in Russia?

Manuela

In part, he does this because Manuela looks like Isabel, partly because he really likes Manuela.


Question: How many times has Manuela been broadcast in Russia?

Manuela

He comes to the village and runs into Rudy, who tells him not to bother Manuela because she has suffered enough because of him.


Question: How many times has Manuela been broadcast in Russia?

Manuela

However, Fernando, now attracted by guilt, breaks into the church during the wedding of Manuela and Rudy just as Manuela must agree.


Question: How many times has Manuela been broadcast in Russia?

Manuela

Seeing Fernando and listening to him, she realizes that she cannot become Rudy's wife.


Question: How many times has Manuela been broadcast in Russia?

Manuela

As a result, a terrible fight takes place between Rudy and Fernando right in front of the church, after which both with severe bruises and wounds end up in Verezzo's house.