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1d
comment What is the number of complex integers inside a circle of radius r?
He means Gausian integer by that.
1d
comment What is the number of complex integers inside a circle of radius r?
en.wikipedia.org/wiki/Gauss_circle_problem
Apr
17
comment Proving a version of maximum modulus principle elementarly.
You can use mean value property of holomorphic function. math.stackexchange.com/questions/72885/…
Apr
15
awarded  Inquisitive
Apr
14
comment What's the Lebesgue measure of this set?
Thanks for solving my misunderstanding. Now the Lebesgue measure looks quite reasonable to me.
Apr
14
comment What's the Lebesgue measure of this set?
Thanks for your answer. Until seeing your comment, I mistakenly assumed that Lebesgue measure satisfies $\sigma$-additivity and concluded that the fact that one point set is measure zero implies any countable set is measure zero. This is clearly because I haven't perused the section 1.5 yet, so I should do as soon as possible.
Apr
14
comment Why are “algebras” called algebras?
Thanks for interesting examples!
Apr
14
accepted Why are “algebras” called algebras?
Apr
14
accepted What's the Lebesgue measure of this set?
Apr
14
comment What's the Lebesgue measure of this set?
That makes sense. I appreciate your answer.
Apr
14
asked What's the Lebesgue measure of this set?
Apr
11
comment properties of connect sets in plane
Consider a punctured disc for the counterexample.
Apr
9
comment How does this inequality of a complex function hold
I greatly appreciate your help.
Apr
9
accepted How does this inequality of a complex function hold
Apr
9
asked How does this inequality of a complex function hold
Apr
3
awarded  Enthusiast
Mar
30
comment Calculate the sum of the following series $\sum_{k=0}^\infty \frac{x^k}{2^k(k+1)!}$
The first one isn't equal to the second one.
Mar
30
comment determine the number of homomorphisms from $D_5$ to $\mathbb{R^*} $ and from $D_5$ to $S_4$
For c), imagine a pentagon with the vertices at the root of $z^5=1$ on complex plane. Let's assign $1$ to the vertex on $z=1$ and assign the next integer to the next vertex counterclockwise. Then, the reflection about real line corresponds to $(2 5)(3 4)$ in $S_5$. The rotation corresponds to $(1 2 3 4 5)$. These two elements in $S_5$ generate a subgroup of $S_5$, so this is an injective homomorphism.
Mar
30
comment Prove: $G \cong M \times N$ and $G$ is finite $\Rightarrow order(N)$ is not divisible by 5
For a), it's easy to show that $\phi:M\times N\to MN$ s.t. $\phi(m,n)=mn$ is an isomorphism, since $MN$ is a subgroup of $G$ because $mn=nm$ $\forall m\in M$ and $\forall n\in N$. Since $|MN|=\frac{|M||N|}{|M\cap N|}=|M||N|=|M||G|/|M|=|G|$, $MN=G$. Thus, $G\simeq M\times N$.
Mar
30
comment String Theory: What to do?
Thanks for your response. As a mathematician, I do not like phenomenological stuffs so much. They are tedious and mathematically not stimulating for me. I'm glad to know that these texts are not usually needed for a string theorist or those with interest in TOE.