# 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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### Proving sequence converges

I am trying to prove: Suppose that {an} and {bn} are two sequences such that {an} and {an + bn} converge. Prove that {bn} converges. Here is my first attempt: Proof: Suppose that {$a_n$} and {$b_n$} ...
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### Prove if $f$ is continuous at a and $g$ is discontinuous at a, then $f + g$ is discontinuous at a

Hello I want to prove: if $f$ is continuous at $a$ and $g$ is discontinuous at $a$, then $f + g$ is discontinuous at $a$. But with the $\epsilon - \delta$ definition of continuity and discontinuity (I ...
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### Most complicated proof of Pythagoras

Usually a mathematician aims for clarity and elegance when conducting a proof. However, the antimathematician buries all hope of assimilating intuition and reasoning. To illustrate this, I seek the ...
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### $fg\in L^1$ for every $g\in L^1$ prove $f\in L^{\infty}$

Let $(X,\mathcal{A}, \mu)$ be an arbitrary measure space. Let $f$ be an extended complex-valued $\mathcal{A}-$measurable function on $X$ such that $|f|<\infty$ $\mu$-a.e. on $X$. Suppose that ...
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### Theoretical Math Sequence Proof

Suppose that {xn} is a sequences such that every subsequence {xni} has a subsequence {xnmi} that converges to x. Show that {xn} is bounded. I tried to do a proof by contradiction but am not sure if ...
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### Proving that $z^4-6z^2+4z-3 = y^2$ has only one integer solution

I'm trying to prove the following result. Conjecture. If $z$ is an integer, and $z^4-6z^2+4z-3$ is a square, then $z=3$. A quick check modulo $9$ shows that $z=9w+3$ for some integer $w$. So for ...
### square matrix $\mathbf{A}$ with $\mathbf{A}^\intercal = -\mathbf{A}$, proof $\mathbf{A}$ is not invertible.
I tried proving that given a square $\mathbf{A}$ over $\mathbb{R}$ so that $\mathbf{A}^\intercal = -\mathbf{A}$, $\mathbf{A}$ is not invertible. I know that because the matrix is real and its ...