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Apr
12
comment Determine the units of the ring $A= \mathbb Z[X]/(X^3)$ and the structure of the group $A^*$
@RobertLewis thanks : )
Apr
12
answered Determine the units of the ring $A= \mathbb Z[X]/(X^3)$ and the structure of the group $A^*$
Apr
8
comment Is a compact, simply-connected 3-manifold necessarily $S^3$ with $B^3$'s removed?
Modulo this "half lives, half dies"-business, you've convinced me about the fact that the boundary is composed of spheres.
Apr
6
answered How to prove that $ \sum_{k=1}^{n-1} \frac{1}{1-e^{2 \pi i k/n}} = \frac{n-1}{2}$?
Apr
6
comment $\frac{1}{2}!$ aka $\Gamma(\frac{3}{2})$
$\Gamma(\frac12)=\sqrt{\pi}$ is a classical result, and the fuctional equation $x\Gamma(x)=\Gamma(x+1)$ gives you the result. Is this the sort of thing you are looking for?
Apr
5
comment Prove $X$ is a complete vector space $\iff$ $\Big[\quad\sum_{n=1}^\infty \| x_n \| \implies \sum_{n=1}^\infty x_n$ converges$\quad\Big]$
Have you looked at some standard textbooks?
Apr
5
comment Continuity of left derivative implies differentiability?
The question you link to is very related, but it's not quite the same, as only continuity at one point $x$ is hypothesized. Can the solution be modified?
Apr
5
answered If $a_i\geq 0,$ $\sum\limits_{n=1}^\infty a_n$converges, prove $\sum\limits_{n=1}^\infty\frac{a_1+a_2+\cdots+a_n}{n}$diverges.
Apr
4
comment Show that no non-trivial open set in $\mathbb{R}^n$ has measure zero in $\mathbb{R}^n$
@user228695 $A$ isn't open in $\Bbb R^2$.
Apr
2
revised Dual of a matrix lie algebra
added 23 characters in body
Apr
2
comment $\sum a_{2n} $ converges
Useful examples of converging, non absolutely converging series arise from alternating series. I wonder why people are downvoting...
Apr
2
comment Is a variety a CW-complex?
For manifolds this is part of Morse theory.
Apr
1
comment Differential-Geometry question- Curve Theory
No problem : ) ${}$
Apr
1
comment Differential-Geometry question- Curve Theory
Then why not edit the question accordingly?
Apr
1
comment Differential-Geometry question- Curve Theory
Should this be an equality?
Apr
1
answered Prove that $ \int_0^\infty (\frac{\sin x}{x})^2 = \frac{\pi}{2}$.
Mar
31
comment Let $|f(z)| \to \infty$ as $|z| \to \infty$, prove that $f(\mathbb{C})= \mathbb{C}$?
@Socchi for any $a\in\Bbb C$ and $\rho>0$ set $\overline{D(a,\rho)}=\lbrace z\in\Bbb C\mid|z-a|\leq\rho\rbrace$The $r$ comes from the fact that $\overline{D(0,R)}$ is compact, so is its image under the continuous map $f$, and so it is closed, i.e. its complement is open, and $a$ lies in that complement.
Mar
31
revised Let $|f(z)| \to \infty$ as $|z| \to \infty$, prove that $f(\mathbb{C})= \mathbb{C}$?
deleted 39 characters in body
Mar
31
comment Let $|f(z)| \to \infty$ as $|z| \to \infty$, prove that $f(\mathbb{C})= \mathbb{C}$?
@Chappers Continuity gives you this.
Mar
31
answered Let $|f(z)| \to \infty$ as $|z| \to \infty$, prove that $f(\mathbb{C})= \mathbb{C}$?