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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 $L^2$, $H^1_0$, … $H^k_0$
Mar
13
comment (Question) on Time-dependent Sobolev spaces for evolution equations
Thank you very much, your explanation is very helpful to me.
Mar
13
accepted (Question) on Time-dependent Sobolev spaces for evolution equations
Mar
12
answered What is happening in a linear algebra computation?