query: Why is $0\cdot x$ defined in fields even though $F\setminus\{0\}$ is the set for multiplication
positive_passages.docid: 26055
positive_passages.text: Multiplication by $0$ in a field
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
negative_passages.docid: 99788
negative_passages.text: Why does a multiplicative subgroup of a field have to be cyclic?
negative_passages.docid: 111515
negative_passages.text: Proving that $-a=(-1)\cdot a$
negative_passages.docid: 113345
negative_passages.text: Why do we set $x^0 = ct$ instead of $x^0 = t$?
negative_passages.docid: 21431
negative_passages.text: The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
negative_passages.docid: 10313
negative_passages.text: Why Multiplication of zero by any number is zero?
negative_passages.docid: 30936
negative_passages.text: Does the operator $(\hat{f}\cdot m )^\vee$ maps Schwartz in it self?
negative_passages.docid: 63280
negative_passages.text: Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition.
negative_passages.docid: 19962
negative_passages.text: Why is $\infty \cdot 0$ not clearly equal to $0$?
negative_passages.docid: 14270
negative_passages.text: Polynomial divisibility is unchanged by coeff. field extension
negative_passages.docid: 69515
negative_passages.text: If $x_n\cdot y_n\to 0$ then $x_n \to 0$ or $y_n \to 0 $
negative_passages.docid: 114813
negative_passages.text: Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
negative_passages.docid: 25050
negative_passages.text: To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
negative_passages.docid: 56817
negative_passages.text: How do you get \mathbb{1} to work (characteristic function of a set)?
negative_passages.docid: 98933
negative_passages.text: Calculating the sum of $f(x) = \sum_{n=0}^{\infty} {n \cdot 2^n \cdot x^n}$
negative_passages.docid: 37041
negative_passages.text: Why is $\text{Aut}(F)$ of the forgetful functor $F$ on $G$-sets isomorphic to $G$?