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Does anyone know a simple proof for the fundamental theorem of finitely generated abelian group?

I am looking for a simple/short proof for the fundamental theorem of finitely generated abelian group. Let $(G,\ +)$ be an abelian group. Assume $G$ is fi...

Published: Aug 28, 2026

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Wedge Sum Example

I am trying to understand the concept of wedge sum in the context of Algebraic Topology. Say I am given two sets, $A=[1, 2, 3]$ and $B=[4, 5]$ Now, disjoi...

Published: Aug 28, 2026

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using fsolve to solve non-linear equations in matlab

I'm trying to solve this system equations in matlab syms y z i x=[29.6,29.4,34.4,35.1,34.3,36.1,31.6,32.9,31.5,28.3,37.1,28.4,27.3,33.1,31.3,33.1] n ...

Published: Aug 28, 2026

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Is this the correct notation?

$\left [ \left \{ 1,2,3,4 \right \}! \right]^{-1}$Is this the correct notation if one wanted to obtain the factorial for each number in a sequence and the...

Published: Aug 28, 2026

$Why does the sum of inverse squares equal $\pi^2/6$? [duplicate]$

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Why does the sum of inverse squares equal $\pi^2/6$? [duplicate]

I've heard that $1+1/4+1/9+1/16+1/25+...$ converges to $\pi^2/6$. This was very surprising to me and I was wondering if there was a reason that it co...

Published: Aug 28, 2026

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"Inverse" of a step function

How can I write the function below $$f(x)=\left\{\begin{array}{ll} 1, & 0\leq t\leq 1, \\ 0, & t>1 \end{array}\right.$$ using the unit step fun...

Published: Aug 28, 2026

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How to calculate recurring probability

I have a very basic understanding of statistics and probability. I just passed an intro college course on it. The problem is, there's one type of pro...

Published: Aug 28, 2026

$How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?$

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How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?

If we have a function $f:A \rightarrow B$, then one way to give meaning, I think, to this function, in terms of set theory, is to say, that $f$ is actuall...

Published: Aug 28, 2026

general

Find the 12th term and the sum of the first 12 terms of a geometric sequence.

A geometric series has a first term $\sqrt{2}$ and a second term $\sqrt{6}$ . Find the 12th term and the sum of the first 12 terms. I can get to the answe...

Published: Aug 28, 2026

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Intuition for dense sets. (Real analysis)

I have been having problems with dense sets as my lecturer didn't really develop an intuition for dense sets in my class. So can any of you please he...

Published: Aug 28, 2026

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