List questions from proof-writing

Published on 14 Apr 2026 - 4:11

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Prove that for all integers $n$ if $3 \mid n^2$, then $3 \mid n$

Published on 15 Apr 2026 - 0:53

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Proving $f$ is continuous if $f_1$ and $f_2$ are continuous and the reciprocal

Published on 13 Apr 2026 - 22:28

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Prove $p \lor q \Leftrightarrow (\neg p) \rightarrow q$, but with caveats.

Published on 24 Apr 2026 - 14:40

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A visible sketch of a proof of the fundamental theorem of algebra

Published on 09 Apr 2026 - 13:06

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Prove or disprove that there is a rational number $x$ and an irrational number $y$ such that $x^y$ is irrational.

Published on 17 Apr 2026 - 14:34

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Proving an Identity using Combinatorial Arguments

Published on 12 Apr 2026 - 10:01

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$\forall{x}\in\mathbb{Z}$, if $\forall{x}\in\mathbb{N}$, $a^x\mid{x}$, then $a=1$ or $a=-1$.

Published on 15 Apr 2026 - 1:40

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Set theory proofs

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Filtered colimits in the category of sets: an equivalence relation

Published on 16 Apr 2026 - 16:21

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Proof Writing: Handshakes in a Party

Published on 11 Apr 2026 - 14:28

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In a given vector space V the zero vector is unique

Published on 14 Apr 2026 - 10:45

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Proof that the Sum of Products is Zero

Published on 14 Apr 2026 - 5:16

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Proving a linear map to be injective and/or surjective

Published on 16 Apr 2026 - 8:46

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An attempted proof of Cauchy's theorem for abelian groups using composition series.

Published on 08 Apr 2026 - 18:38

List Question

Show that the set of all algebraic numbers over the field of rationals is countable

Prove that for all integers $n$ if $3 \mid n^2$, then $3 \mid n$

Proving $f$ is continuous if $f_1$ and $f_2$ are continuous and the reciprocal

Prove $p \lor q \Leftrightarrow (\neg p) \rightarrow q$, but with caveats.

A visible sketch of a proof of the fundamental theorem of algebra

Prove or disprove that there is a rational number $x$ and an irrational number $y$ such that $x^y$ is irrational.

Proving an Identity using Combinatorial Arguments

$\forall{x}\in\mathbb{Z}$, if $\forall{x}\in\mathbb{N}$, $a^x\mid{x}$, then $a=1$ or $a=-1$.

Set theory proofs

Filtered colimits in the category of sets: an equivalence relation

Proof Writing: Handshakes in a Party

In a given vector space V the zero vector is unique

Proof that the Sum of Products is Zero

Proving a linear map to be injective and/or surjective

An attempted proof of Cauchy's theorem for abelian groups using composition series.

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