query: Prove that in an ordered field, $0\cdot x=0$ for every $x$
positive_passages.docid: 151011
positive_passages.text: Fields - Proof that every multiple of zero equals zero
negative_passages.docid: 134043
negative_passages.text: Prove that for $ f(x+2\cdot\pi)=f(x), x \in \mathbb{R} $, there exists $ x_0 $ so $ f(x_0+\pi)=f(x_0) $
negative_passages.docid: 1141
negative_passages.text: Existence of totally ordered ring with zero divisors
negative_passages.docid: 62012
negative_passages.text: What is $0\div0\cdot0$?
negative_passages.docid: 70776
negative_passages.text: Characteristic of a field is $0$ or prime
negative_passages.docid: 88676
negative_passages.text: Proof verification : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability
negative_passages.docid: 154459
negative_passages.text: Constructing a HoTT proof term of 1≠0
negative_passages.docid: 7448
negative_passages.text: Prove $S \doteq \sum_{n=1}^{\infty} p_n  0$ assuming $0 \leq p_n < 1$.
negative_passages.docid: 140474
negative_passages.text: Why is Ext$(-;k) =0$ when $k$ is a field
negative_passages.docid: 33989
negative_passages.text: If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.
negative_passages.docid: 86626
negative_passages.text: Finite fields, existence of field of order $p^n$,proof help
negative_passages.docid: 7813
negative_passages.text: In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
negative_passages.docid: 116856
negative_passages.text: Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
negative_passages.docid: 138083
negative_passages.text: $\gcd(X^n - 1, nX^{n-1}) = 1$ in a field $K$ of characteristic $0$ or characteristic $p \nmid n$.
negative_passages.docid: 155974
negative_passages.text: Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
negative_passages.docid: 120010
negative_passages.text: Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
negative_passages.docid: 11715
negative_passages.text: Prove that if $\langle Tx,x\rangle =0$ for all $x \in X$, then $T = 0$