Tagged Questions

If you already have a proof for some result, but want to ask for a different proof (using different methods).

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Multidimensional Cantor diagonal argument for ordering infinite sets [duplicate]

Cantor diagonal argument is a powerful proof technique. It has been used for a lot of proofs. For instance, it has been used to prove that $|\mathbb{N}| < |\mathbb{R}|$. What can we say about the ...
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A purely algebraic proof of $\vec{a}\cdot \vec{b} = \lVert\vec{a} \rVert\lVert\vec{b} \rVert\cos(\theta)$

I have seen a proof of the fact that $$\vec{a}\cdot \vec{b} = \lVert\vec{a} \rVert\lVert\vec{b} \rVert\cos(\theta)$$ where $\vec{a}$ and $\vec{b}$ are two vectors. The proof relies on the Law of ...
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Unramified at a point $x \in X$ if and only if $\Omega _{X,x} = 0$

This is Corollary 6.2.3 in Liu's book. Let $f: X \to S$ be a morphism of finite type of locally Noetherian schemes. Then $f$ is unramified at a point $x \in X$ if and only if $\Omega_{X/S, x} = 0$....
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Alternative Proof: if $n$ is an integer, prove that $\frac{n ( n^4 - 1)}{5}$ is an integer

I have proven this by the induction method but would like to know if it can be proven using an alternative method.
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Probability space for zebras and their number of stripes

On a trip to Africa the researcher Alison notices that zebras with an even amount of stripes have double the probability to be seen than zebras with an odd amount of stripes. Let $E_n$ denote the ...
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Show that finite dimensional subspace is closed

We know that if $V$ is a normed vector space and $W$ is a finite dimensional subspace of $V$, then $W$ is closed. One way to prove this is to show that $W$ is actually complete. Since complete space ...
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Prove directly from definition: countably compact subsets of metric spaces are closed

I am trying to prove the statement that every countably compact subset Y of a metric space (X,d) is closed. I am aware of the fact that, for metric spaces, countable compactness is equivalent to ...
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Prove that the equation $x^4 = y^2 +z^2 +4$ has no integer solutions.
Prove that the equation $x^4 = y^2 +z^2 +4$ has no integer solutions. I believe I have proved it for the case when both $y$ and $z$ are of the same parity. Case 1: When $y$ and $z$ are of the same ...
Prove $\sinh x > x$ for all $x >0$
I did a proof for $\sinh x > x$ for all $x > 0$. But I am not sure if the proof is mathematically valid. I started by showing that $\frac{d}{dx} \sinh x = \cosh x$ and that the limit of \$\cosh ...