# Zango Lotino

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 Sep24 awarded Autobiographer Jan8 awarded Yearling Nov29 awarded Organizer Nov29 revised Tensor product, Artin-Rees lemma and Krull intersection theorem I added a new tag. Nov29 suggested suggested edit on Tensor product, Artin-Rees lemma and Krull intersection theorem Nov3 awarded Nice Answer Apr28 accepted Let $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$ be differentiable a.e. Is $x \rightarrow Df(x)$ a Borel measurable function? Apr28 comment A continuous function from $\mathbb{R}$ to $\mathbb{R}$ that has fixed points at $kn^2$ where $n$ is prime and $k$ is integer It makes no sense computing taylor series for a function that is not differentiable. Anyway, if you compute it in a neighbourhood of everypoint outside $A$ and $B$, then surely taylor series coincides with the function in that neighbourhood and all terms in the series but first and second will be $0$. Apr28 asked Let $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$ be differentiable a.e. Is $x \rightarrow Df(x)$ a Borel measurable function? Apr28 comment A continuous function from $\mathbb{R}$ to $\mathbb{R}$ that has fixed points at $kn^2$ where $n$ is prime and $k$ is integer As Clayton says, imagine you draw images for points in $A$ and $B$, now join those points by segments and you get the desired function. It is continuous by construction. Apr28 revised A continuous function from $\mathbb{R}$ to $\mathbb{R}$ that has fixed points at $kn^2$ where $n$ is prime and $k$ is integer added 93 characters in body Apr28 answered A continuous function from $\mathbb{R}$ to $\mathbb{R}$ that has fixed points at $kn^2$ where $n$ is prime and $k$ is integer Apr12 awarded Necromancer Jan18 revised The facts about $\varphi$ deleted 341 characters in body; edited title Jan17 revised The dimension of linear map added 32 characters in body Jan17 revised The dimension of linear map added 95 characters in body Jan17 comment The dimension of linear map Since it is parametrized from $v \in P$ you can identify it with $P$ and $P$ is a k-dimensional subspace of $V$. Jan17 comment The dimension of linear map Observe that a linear map is also a continuous function with respect to the topology induced by a norm in that vector space. Jan17 comment The dimension of linear map What I try to point out is that both definitions are the same, with different notation: $v+Xv =(v, X(v))$ Jan17 answered The dimension of linear map