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# Questions tagged [solution-verification]

For posts looking for feedback or verification of a proposed solution. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.

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### Law of Large Numbers for a Brownian Motion

I am self-learning introductory stochastic calculus from A first course in Stochastic Calculus by L.P.Arguin. The part(c) of the below exercise problem on the time-inversion property of Brownian ...
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### Proving $\mathbb{R}$ is a subfield of $\mathbb{C}$: Is preservation of operations necessary?

I'm reading Rudin's book where he defines the complex field, initially as ordered pairs $(a,b)$. I'm trying to prove the assertion that $\mathbb{R}$ is a subfield of $\mathbb{C}$. I unfortunately ...
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### Proof attempt for a weaker form of the Collatz Conjecture

I am kind of new to this problem and I tried solving it with open mind. Please don't be judgmental, this is what I got. Let us assume, for the sake of contradiction, that the Collatz conjecture is ...
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### Find the determinants of A by row reduction to echelon form.

When I try to solve this question, it keeps ending with reduced echelon form, not to echelon form, where all diagonals are zero. And, I get detA = 10. Is this correct? Thank you.
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### If $\mathbb{V}$ is a vector space, is it always true that $\mathbb{V} = \text{span}(\mathbb{V})$?

This question have just came to my mind after starting to study some linear algebra. I tried to write the following proof: Let $\mathbb{V}$ be a vector space. ($\subseteq$) Let $v \in \mathbb{V}$. We ...
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### Incorrect proof: $\frac32-\frac{\pi^2}6=\sum_{k=1}^\infty\frac{(k+1)!B_{2k}}{(2k)!}$

I incorrectly proved that $$\frac32-\sum_{k=1}^\infty\frac{(k+1)!B_{2k}}{(2k)!}=\frac{\pi^2}6$$According to Wolfram Alpha, the LHS is approximately $1.34096$, while $\frac{\pi^2}6\approx1.64493$. Here ...
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### Do unit quaternions admit a continuous square root function?

Let $G$ be a multiplicative group. A function $\text{sqrt}: G \to G$ is a square root function iff, for every $x \in G$, $(\text{sqrt}(x))^2 = x$. The unit real numbers, namely $\pm 1$, doesn't even ...
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### $N$ coins placed randomly on vertices of $M$-sided regular polygon. Find expected value and var. of the number of sides with coins on both vertices.

There are $N$ coins, $N \geq 1$. We place them randomly on vertices of $M$-sided regular polygon, $M \geq N$, in every vertice there is at most $1$ coin. We call X the number of sides with coins on ...
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