Does there exist a function $f$ on an open set $G\subset\mathbb{R}^2$ , which $f_x$ and $f_y$ exist everywhere but $f$ is nowhere differentiable in $G$?
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So if I have a matrix and I put it into RREF and keep track of the row operations, I can then write it as a product of elementary matrices. ...
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I am asked to prove the density of irrationals in $\mathbb{R}$. I understand how to do this by proving the density of $\mathbb{Q}$ first, na...
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