Alexei Averchenko
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 Jan21 awarded Popular Question Jan5 awarded Popular Question Nov21 awarded Yearling Nov13 awarded Necromancer Nov3 awarded Favorite Question Oct9 awarded Popular Question Sep30 awarded Explainer Sep24 awarded Autobiographer Aug14 revised How can I prove that $xy\leq x^2+y^2$? added 637 characters in body Aug14 comment How can I prove that $xy\leq x^2+y^2$? @ronno Not really, because $X := \mathbb{R}^2 \setminus \{x = -y\}$ is dense in $\mathbb{R}^2$, and $[0, +\infty)$ is closed in $\mathbb{R}$, therefore its pullback along $(x, y) \mapsto x^2 - xy + y^2$ must be $\operatorname{cl}X = \mathbb{R}^2$. Of course it is too technical for a precalculus-level question. Jul2 awarded Curious Jul2 awarded Inquisitive May10 awarded Good Question Mar30 revised How can I prove that $xy\leq x^2+y^2$? Removed dickishness Feb20 awarded Popular Question Nov21 awarded Yearling Nov16 awarded Notable Question Aug19 comment Rigour in mathematics @RobertIsrael Suppose there is a proposition, and you can prove that it is impossible to construct a counterexample to it. Is this proposition true? Aug17 awarded Nice Answer Aug11 answered Rigour in mathematics