# All Questions

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### prime cycle in permutation groups

I'm trying to use the jordan theorem and for that we need find the prime cycle on permutation group which i don't have idea how to find it . (my English is poor, so sorry for this)
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### Expectation of the infimum of a GBM

does somebody know a reference, where I can find the value of the expectation of the running infimum of a geometric Brownian motion, namely: Given a filtered probability space ...
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### Converge of Sum divide by log(n)

I am trying to show that If $b_n = \sum^n_{k=1}(k^{-1}) -\sum^n_{k=1}(k^{-2})$ then $\frac{b_n}{\log(n)} \rightarrow 1$ as $n \rightarrow \infty$ I start this problem by showing this inequality ...
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### Irrational numbers to the power of other irrational numbers: A beautiful proof question

The following theorem has a very beautiful proof. Theorem: There exist two irrational numbers $x$ and $y$ such that $x^y$ is rational. Proof: If $\sqrt{2}^{\sqrt{2}}$ is rational then we ...
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### Prove that If $X$ be compact with co-countable topology, then X is finite.

Prove that If $X$ be compact with co-countable topology, then X is finite.
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### How does one find a minimal primary decomposition?

What exactly does it mean for a primary decomposition to be "minimal" and is the a general method to obtain such decompositions? I've tried looking at some examples but they all give very little ...
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### How do I solve operations involving fractional surds?

I want to know how to independently solve operations involving fractional surds such as this: How do I logically figure out how to do each one? I can do some of them, but not all of them. Do I ...
### If $A^TA$ is invertible, then $A$'s columns are linearly independent (not necessarily square matrix)
My textbook wants me to verify that when $A^TA$ is invertible, then $A$'s columns are linearly independent. However, I may not assume that $A$ is invertible, or even square. How should I go about?