List questions from proof-writing

Published on 15 Apr 2026 - 5:35

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Adding fractions of unlike denominators

Published on 11 Apr 2026 - 13:21

456

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Write $2+\log_3 x+\log_9 x^4-\log_{27} x^5$ into one single logarithm

Published on 17 Apr 2026 - 12:45

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What are the number of solutions of $|\sqrt{2\sin^4 x+18\cos^2 x}-\sqrt{2\cos^4 x+18\sin^2 x}|=1?$

Published on 15 Apr 2026 - 21:17

356

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How can one prove this property of integrals?$\int_0^bf(x)(b-x)\,dx=\int_0^b\left(\int _0^xf(t)\,dt\right)\,dx$

Published on 16 Apr 2026 - 8:06

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Prove that vectors are parallel iff their unit vectors are equal

Published on 08 Apr 2026 - 22:51

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Is this an "If and only if" proof?

Published on 13 Apr 2026 - 23:27

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$\mathbb{R}^n$ Second Countable

Published on 10 Apr 2026 - 23:58

72

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How to write a proper, rigorous proof: Colouring vertices on a line graph

Published on 14 Apr 2026 - 14:19

382

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The eigenvalue of Lie bracket

Published on 12 Apr 2026 - 15:39

326

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Prove the following inequality for any positive real number $x,y$

Published on 14 Apr 2026 - 1:28

146

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Proving $\cos2A+\cos2B-\cos2C=1-4\sin A\sin B\cos C$ with identities for $\sin2A+\sin2B+\sin2C$ and $\cos2A+\cos2B+\cos2C$

Published on 15 Apr 2026 - 23:38

52

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How can I prove that m, n in $m^2 = 6n^2$ are not integers?

Published on 15 Apr 2026 - 3:36

34

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Limiting ratio for the distance between a step and the step itself

Published on 14 Apr 2026 - 5:43

342

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Is a "Definition" a statement or a sentence?

Published on 10 Apr 2026 - 15:39

List Question

Given that $\theta=45°$, find $\angle AOC$.

Adding fractions of unlike denominators

Write $2+\log_3 x+\log_9 x^4-\log_{27} x^5$ into one single logarithm

What are the number of solutions of $|\sqrt{2\sin^4 x+18\cos^2 x}-\sqrt{2\cos^4 x+18\sin^2 x}|=1?$

How can one prove this property of integrals?$\int_0^bf(x)(b-x)\,dx=\int_0^b\left(\int _0^xf(t)\,dt\right)\,dx$

Prove that vectors are parallel iff their unit vectors are equal

Is this an "If and only if" proof?

$\mathbb{R}^n$ Second Countable

How to write a proper, rigorous proof: Colouring vertices on a line graph

The eigenvalue of Lie bracket

Prove the following inequality for any positive real number $x,y$

Proving $\cos2A+\cos2B-\cos2C=1-4\sin A\sin B\cos C$ with identities for $\sin2A+\sin2B+\sin2C$ and $\cos2A+\cos2B+\cos2C$

How can I prove that m, n in $m^2 = 6n^2$ are not integers?

Limiting ratio for the distance between a step and the step itself

Is a "Definition" a statement or a sentence?

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