Aran Komatsuzaki
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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 Apr17 comment Proving a version of maximum modulus principle elementarly. You can use mean value property of holomorphic function. math.stackexchange.com/questions/72885/… Apr15 awarded Inquisitive Apr14 comment What's the Lebesgue measure of this set? Thanks for solving my misunderstanding. Now the Lebesgue measure looks quite reasonable to me. Apr14 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. Apr14 comment Why are “algebras” called algebras? Thanks for interesting examples! Apr14 accepted Why are “algebras” called algebras? Apr14 accepted What's the Lebesgue measure of this set? Apr14 comment What's the Lebesgue measure of this set? That makes sense. I appreciate your answer. Apr14 asked What's the Lebesgue measure of this set? Apr11 comment properties of connect sets in plane Consider a punctured disc for the counterexample. Apr9 comment How does this inequality of a complex function hold I greatly appreciate your help. Apr9 accepted How does this inequality of a complex function hold Apr9 asked How does this inequality of a complex function hold Apr3 awarded Enthusiast Mar30 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. Mar30 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. Mar30 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, $G\simeq M\times N$. Mar30 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.