List questions from proof-explanation

Published on 31 Dec 2018 - 21:26

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Understanding lemma for proof of convexity

Published on 31 Dec 2018 - 23:29

51

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Consider the function $θ:\{0,1\}×{\Bbb N}→{\Bbb Z}$ defined as $θ(a,b)=(-1)^{a}b$

Published on 01 Jan 2019 - 8:36

439

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Prove that for all integers $x$ with final digit equal to $5$, $x$ is a multiple of $5$

Published on 01 Jan 2019 - 13:17

886

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Prove that if $m$ divide $n$ then $x^{p^{m-1}}-1$ divide $x^{p^{n-1}}-1$

Published on 01 Jan 2019 - 15:52

42

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Proving finite bases for a Harshad number?

Published on 02 Jan 2019 - 0:48

206

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Example 6.18. from the book of Algebra by Aluffi

Published on 30 Mar 2026 - 14:01

87

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What does this set-theoretic notation mean in the proof of this theorem?

Published on 26 Mar 2026 - 13:57

162

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Proof in EGA I Chapter 0, point 3.2.2

Published on 26 Mar 2026 - 14:19

347

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Understanding Graham's proof of theorem on Unit Fractions.

Published on 25 Mar 2026 - 17:19

930

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Proof explanation of $``\exists x\in\mathbb{R}$ with $x^2=2"$

Published on 28 Mar 2026 - 22:27

57

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Understanding a proof about Hausdorff spaces.

Published on 04 Jan 2019 - 2:58

44

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sets theory-Realation proof question

Published on 26 Mar 2026 - 22:19

98

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$Q(n)$: "$P(k)$ holds for all $k<n$". Then why is $Q(0)$ clearly true?

Published on 30 Mar 2026 - 7:11

1.1k

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How to use the terms "fixed", "arbitrary", "fixed but arbitrary", "given", "for all" ... in proofs

Published on 30 Mar 2026 - 7:07

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Complex inequality $|a+b|\le |a|+|b|$

Understanding lemma for proof of convexity

Consider the function $θ:\{0,1\}×{\Bbb N}→{\Bbb Z}$ defined as $θ(a,b)=(-1)^{a}b$

Prove that for all integers $x$ with final digit equal to $5$, $x$ is a multiple of $5$

Prove that if $m$ divide $n$ then $x^{p^{m-1}}-1$ divide $x^{p^{n-1}}-1$

Proving finite bases for a Harshad number?

Example 6.18. from the book of Algebra by Aluffi

What does this set-theoretic notation mean in the proof of this theorem?

Proof in EGA I Chapter 0, point 3.2.2

Understanding Graham's proof of theorem on Unit Fractions.

Proof explanation of $``\exists x\in\mathbb{R}$ with $x^2=2"$

Understanding a proof about Hausdorff spaces.

sets theory-Realation proof question

$Q(n)$: "$P(k)$ holds for all $k<n$". Then why is $Q(0)$ clearly true?

How to use the terms "fixed", "arbitrary", "fixed but arbitrary", "given", "for all" ... in proofs

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