query: If $|a|$, $|b|$ is finite then $|ab|$ is finite?
positive_passages.docid: 8742
positive_passages.text: Examples and further results about the order of the product of two elements in a group
negative_passages.docid: 113211
negative_passages.text: Arithmetics of cardinalities: if $|A|=|C|$ and $|B|=|D|$ then $|A\times B|=|D\times C|$
negative_passages.docid: 147013
negative_passages.text: Subset of a finite set is finite
negative_passages.docid: 76049
negative_passages.text: Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
negative_passages.docid: 105367
negative_passages.text: Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
negative_passages.docid: 94413
negative_passages.text: Proving Dedekind finite implies finite assuming countable choice
negative_passages.docid: 49592
negative_passages.text: Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto.
negative_passages.docid: 13012
negative_passages.text: Why can a = b imply 2 = 1?
negative_passages.docid: 67483
negative_passages.text: Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
negative_passages.docid: 158590
negative_passages.text: Why is it that if $[L:K]$ is finite, then $[L:K]$ is algebraic?
negative_passages.docid: 139934
negative_passages.text: In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
negative_passages.docid: 142855
negative_passages.text: If $A$, $B$ are both pairwise independent of $C$, do we have that $A \cap B$ is also independent of $C$?
negative_passages.docid: 20335
negative_passages.text: If $A\subset B$ then $\bar{A}\subset \bar{B}$
negative_passages.docid: 32402
negative_passages.text: $(A \implies B) \implies (\neg B \implies \neg A)$?
negative_passages.docid: 143979
negative_passages.text: How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
negative_passages.docid: 138707
negative_passages.text: show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
negative_passages.docid: 88201
negative_passages.text: Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective.