List questions from proof-explanation

Published on 12 Apr 2026 - 0:42

189

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A positive-definite binary quadratic form represents an odd prime $p$ if and only if $p \equiv 1 \pmod 4$.

Published on 16 Apr 2026 - 8:25

473

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Explanation of Brouwer fixed point theorem in one dimension.

Published on 13 Apr 2026 - 13:18

25

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Integrability proof

Published on 14 Apr 2026 - 16:11

97

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Difficulty with proof of Spectral Theorem

Published on 25 Apr 2026 - 3:38

294

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Show that $SO_{3}$ contains the free group of rank 2 as a subgroup.

Published on 15 Apr 2026 - 22:07

37

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About certain proof of countability of $\mathbb{Q}$

Published on 11 Apr 2026 - 22:22

85

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Proof explanation: Spectral radius of operators

Published on 13 Apr 2026 - 6:04

60

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Show that the inequality $\frac{s}{t} + \frac{t}{r} + \frac{r}{s} >= 3$, assuming s,t,r >0.

Published on 28 Mar 2026 - 0:06

524

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Equality of Bernoulli's inequality

Published on 14 Apr 2026 - 15:08

155

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Proving $(x, y, z) \mapsto (2x + y, 2y − z)$ is linear

Published on 14 Apr 2026 - 0:40

63

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Prove a recursively defined function property by induction

Published on 14 Apr 2026 - 21:43

52

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Prove that $\sim$ is an equivalence relation on $\mathcal{P}(X)$

Published on 14 Apr 2026 - 23:33

126

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Show $\frac{\sqrt{\sqrt[4]8-\sqrt{\sqrt2+1}\;}}{\sqrt{\sqrt[4]8+\sqrt{\sqrt2-1}\;} -\sqrt{\sqrt[4]8-\sqrt{\sqrt2-1}\;}}=\frac1{\sqrt2}$

Published on 25 Mar 2026 - 23:42

1.6k

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Linear operator continuous if and only if bounded; explanation of idea of proof

Published on 13 Apr 2026 - 4:32

List Question

About two different proofs of Archimedean property

A positive-definite binary quadratic form represents an odd prime $p$ if and only if $p \equiv 1 \pmod 4$.

Explanation of Brouwer fixed point theorem in one dimension.

Integrability proof

Difficulty with proof of Spectral Theorem

Show that $SO_{3}$ contains the free group of rank 2 as a subgroup.

About certain proof of countability of $\mathbb{Q}$

Proof explanation: Spectral radius of operators

Show that the inequality $\frac{s}{t} + \frac{t}{r} + \frac{r}{s} >= 3$, assuming s,t,r >0.

Equality of Bernoulli's inequality

Proving $(x, y, z) \mapsto (2x + y, 2y − z)$ is linear

Prove a recursively defined function property by induction

Prove that $\sim$ is an equivalence relation on $\mathcal{P}(X)$

Show $\frac{\sqrt{\sqrt[4]8-\sqrt{\sqrt2+1}\;}}{\sqrt{\sqrt[4]8+\sqrt{\sqrt2-1}\;} -\sqrt{\sqrt[4]8-\sqrt{\sqrt2-1}\;}}=\frac1{\sqrt2}$

Linear operator continuous if and only if bounded; explanation of idea of proof

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