query: How to prove the set of functions from the natural numbers to the natural numbers is equinumerous to the set of real numbers
positive_passages.docid: 29065
positive_passages.text: Encode each $n_1,n_2,n_3,...∈N^N$ by an inﬁnite sequence of 0s and 1s with inﬁnitely many 0s, and give a proof that $N^N$ is equinumerous with $R$.
negative_passages.docid: 107248
negative_passages.text: Prove that the set $ \{\sin(x),\cos(x),\sin(2x),\cos(2x)\}$ is linearly independent.
negative_passages.docid: 13273
negative_passages.text: Cardinality of the set of all real functions of real variable
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 116009
negative_passages.text: Proving that if a set is both open and closed then it is equal to the real numbers
negative_passages.docid: 55840
negative_passages.text: Number of functions from n-element set to {1, 2, …, m}
negative_passages.docid: 75007
negative_passages.text: How can I prove this relation between the elementary set theory and the elementary logic?
negative_passages.docid: 36694
negative_passages.text: Sum of first n natural numbers proof
negative_passages.docid: 21820
negative_passages.text: How to prove that a set is invariant?
negative_passages.docid: 130542
negative_passages.text: Every natural number $n$ can be written as $n=s-t$ with $\omega(s)=\omega(t)$
negative_passages.docid: 137883
negative_passages.text: Cardinality of the set of all (real) discontinuous functions
negative_passages.docid: 135315
negative_passages.text: Proving whether a function on the set of real sequences is a metric
negative_passages.docid: 146665
negative_passages.text: Prove that $f(x)=8$ for all natural numbers $x\ge{8}$
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 113083
negative_passages.text: How to prove a set equality?
negative_passages.docid: 99656
negative_passages.text: Prove that the set of all algebraic numbers is countable
negative_passages.docid: 146055
negative_passages.text: Proving a set of functions is uncountable