query: Is this correct approach to proving $xy=0$?
positive_passages.docid: 16948
positive_passages.text: Need help with a proof that if $xy=0$ then $x=0$ or $y=0$
negative_passages.docid: 135087
negative_passages.text: Find integer solutions of $xy=-1$ (using only elementary ring theory).
negative_passages.docid: 31051
negative_passages.text: Is $f(x,y)=(xy)^{2/3}$ differentiable at $(0,0)$?
negative_passages.docid: 156235
negative_passages.text: Are $x \cdot 0 = 0$, $x \cdot 1 = x$, and $-(-x) = x$ axioms?
negative_passages.docid: 151329
negative_passages.text: Showing $\lim_{(x,y) \to (0,0)} \sin (xy) / xy = 1$
negative_passages.docid: 118873
negative_passages.text: Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
negative_passages.docid: 155341
negative_passages.text: Proving or disproving inequality $ \frac{xy}{z} + \frac{yz}{x} + \frac{zx}{y} \ge x + y + z $
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
negative_passages.docid: 120774
negative_passages.text: Show that $f$ has exactly one zero on the square $Q =$ {$x + iy ∈ \Bbb C : |x| < 1, |y| < 1$}.
negative_passages.docid: 127183
negative_passages.text: Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
negative_passages.docid: 83337
negative_passages.text: If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$
negative_passages.docid: 145466
negative_passages.text: Is this a valid mathematical proof?
negative_passages.docid: 2251
negative_passages.text: Can someone give me a hint on how to prove this?
negative_passages.docid: 48935
negative_passages.text: Showing $\lim_{(x,y) \to (0,0)} xy \log(x^2+y^2) = 0$
negative_passages.docid: 154327
negative_passages.text: $A^2X = X$ show that $AX = X$, if $A_{ij} > 0$ and $x_{i} > 0$
negative_passages.docid: 105852
negative_passages.text: How to verify whether or not there exists a vector $x$ such that $Ax > 0$?
negative_passages.docid: 89637
negative_passages.text: Proof that in a field $x=0$ is equivalent to $x=-x$