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 Mar 25 awarded Quorum Mar 24 revised Proof of $f = g \in L^1_{loc}$ if $f$ and $g$ act equally on $C_c^\infty$ edited title Mar 24 asked Proof of $f = g \in L^1_{loc}$ if $f$ and $g$ act equally on $C_c^\infty$ Mar 22 comment Convergence of a series of complex numbers that are dense on the unit circle Let $z_n = e^{2i\pi \theta n}$, with $\theta$ some irrational number. Then $z_n$ is dense on the unit circle and serves your assumptions. But you can easily pick a series of vectors near to $1$, s.t. the series of partial sums diverges into infinity. Doesn't this contradict your postulate? You can make the series convergent of you just choose any order s.t. suceeding elements cancel out each other sufficiently well. But you may miss elements if you construct that sequence. Mar 22 comment Why is the identity map never equal to the product of an odd number of reflections? It might be interesting for you: The product of two reflections is a rotation (look up in Wikipedia). Mar 22 comment Different definitions for submanifolds It's quite late in my country, so the following answer is probably either wrong or bluntly oversophisticated: The map from $V$ to $M$ is differentiable and invertible, in particular the derivative does not vanish. It maps the coordinate directions within the local chart to tangential vectors of the submanifold. Choose a field of $n-n'$ vectors orthogonal to the tangential vector field. Now after possible restriction, vary the slice into the direction of these orthogonal normal vectors. Try to build a chart as in $I$ now. Mar 21 comment Sum of $\sum \limits_{n=1}^{\infty} \frac{2^{2n+1}}{5^n}$ do not pull the $2$ out of each summand, but out of the whole sum. Generally, try get "wild" expressions as clear as possible from non essential stuff. And now learn about the geometric series in Wikipedia. Mar 20 accepted On distributions over $\mathbb R$ whose derivatives vanishes Mar 20 revised On distributions over $\mathbb R$ whose derivatives vanishes explanation Mar 19 asked On distributions over $\mathbb R$ whose derivatives vanishes Mar 19 accepted Topologies on the space $\mathcal D'(U)$ of distributions Mar 19 revised Topologies on the space $\mathcal D'(U)$ of distributions typo Mar 19 asked Topologies on the space $\mathcal D'(U)$ of distributions Mar 18 comment Image Of a Discontinuous linear functional What it is $unit dis$? Is it the unit sphere or the unit ball? Mar 17 comment proof that an alternative definition of limit is equivalent to the usual one In case you are not given this as a definition already, what standard definition do you refer to? Mar 17 revised Proof of Heine-Borel in $\mathbb R^n$ typo; edited body; added 20 characters in body Mar 17 answered Proof of Heine-Borel in $\mathbb R^n$ Mar 14 accepted Simultaneous orthogonal basis for $L^2$, $H^1_0$, … $H^k_0$ Mar 14 accepted Realification and Complexification of vector spaces Mar 14 asked Simultaneous orthogonal basis for $L^2$, $H^1_0$, … $H^k_0$