query: Prove that x and y commute
positive_passages.docid: 43783
positive_passages.text: Abelian group (Commutative group)
negative_passages.docid: 16548
negative_passages.text: Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
negative_passages.docid: 116389
negative_passages.text: If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute
negative_passages.docid: 79040
negative_passages.text: Graph of $|x| + |y| = 1$
negative_passages.docid: 138931
negative_passages.text: Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
negative_passages.docid: 100549
negative_passages.text: If $e^A$ and $e^B$ commute, do $A$ and $B$ commute?
negative_passages.docid: 125209
negative_passages.text: Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
negative_passages.docid: 59644
negative_passages.text: Proof of Cartesian product intersection
negative_passages.docid: 140988
negative_passages.text: Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
negative_passages.docid: 44980
negative_passages.text: Prove that two paths on opposing corners of the unit square must cross.
negative_passages.docid: 54479
negative_passages.text: If $x,y$ are nilpotent and commute, $x+y $ is nilpotent.
negative_passages.docid: 1453
negative_passages.text: Prove that the graph is connected
negative_passages.docid: 95379
negative_passages.text: Prove that $V = V_1 \oplus V_2$ in the following
negative_passages.docid: 50273
negative_passages.text: How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
negative_passages.docid: 12484
negative_passages.text: Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
negative_passages.docid: 142724
negative_passages.text: Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
negative_passages.docid: 12104
negative_passages.text: How to prove this result involving the quotient maps and connectedness?