Question

Proof by cases that there is an irrational number $a$ such that $a^{\sqrt{3}}$ is rational?

score 645 · Answer 1 · 2026-03-25 13:13:33

645

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Proof by cases that there is an irrational number $a$ such that $a^{\sqrt{3}}$ is rational?

Published on 25 Mar 2026 - 13:13

score 204 · Answer 2 · 2026-03-25 12:48:44

204

Views

Understanding the proof of a continuity principle for potentials

Published on 25 Mar 2026 - 12:48

score 231 · Answer 3 · 2026-03-28 22:37:58

231

Views

Alternative form of the calculation of the second partial derivative of an operator

Published on 28 Mar 2026 - 22:37

score 189 · Answer 4 · 2026-03-28 23:20:10

189

Views

Prove that a strongly convex function imples $2c(F(w)-F_*) \leq ||\nabla F(w)||_2^2$

Published on 28 Mar 2026 - 23:20

score 60 · Answer 5 · 2018-05-28 08:00:58

60

Views

Number bases $p$

Published on 28 May 2018 - 8:00

score 269 · Answer 6 · 2026-03-25 09:29:09

269

Views

Use of substitution into the integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$

Published on 25 Mar 2026 - 9:29

score 53 · Answer 7 · 2026-03-25 09:29:53

53

Views

How to calculate the number of ways to climb a building if only $1$ or $2$ floors can be climbed each time with elevator possibility at some floor?

Published on 25 Mar 2026 - 9:29

score 205 · Answer 8 · 2026-03-25 17:31:53

205

Views

On Kelvin-Stokes proof without differential forms

Published on 25 Mar 2026 - 17:31

score 295 · Answer 9 · 2026-03-25 23:27:21

295

Views

Confusion regarding the proof of Theorem I.32 of Apostol's Calculus.

Published on 25 Mar 2026 - 23:27

score 50 · Answer 10 · 2026-03-27 06:56:53

50

Views

Convergence of power series under a given condition

Published on 27 Mar 2026 - 6:56

score 385 · Answer 11 · 2026-03-25 17:45:17

385

Views

Spectral theorem and positive definite inner product

Published on 25 Mar 2026 - 17:45

score 45 · Answer 12 · 2026-03-25 14:24:37

45

Views

how would prove that $\prod_{k=1}^n 1 - 1_{A_k} = \sum_{I \subset \{1,2,...,n\} }(-1)^{card(I)}1_{A_I}$

Published on 25 Mar 2026 - 14:24

score 60 · Answer 13 · 2026-03-25 15:39:41

60

Views

Second exact sequence for closed embedding of nonsingular varieties.

Published on 25 Mar 2026 - 15:39

score 771 · Answer 14 · 2026-03-25 09:53:57

771

Views

In proving every open connected subset of $\mathbb{R}^n$ is path connected

Published on 25 Mar 2026 - 9:53

score 481 · Answer 15 · 2026-03-26 11:05:11

481

Views

IMO 2005 No 4. : All integers relatively prime to terms of infinite sequence

Published on 26 Mar 2026 - 11:05

List Question

Proof by cases that there is an irrational number $a$ such that $a^{\sqrt{3}}$ is rational?

Understanding the proof of a continuity principle for potentials

Alternative form of the calculation of the second partial derivative of an operator

Prove that a strongly convex function imples $2c(F(w)-F_*) \leq ||\nabla F(w)||_2^2$

Number bases $p$

Use of substitution into the integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$

How to calculate the number of ways to climb a building if only $1$ or $2$ floors can be climbed each time with elevator possibility at some floor?

On Kelvin-Stokes proof without differential forms

Confusion regarding the proof of Theorem I.32 of Apostol's Calculus.

Convergence of power series under a given condition

Spectral theorem and positive definite inner product

how would prove that $\prod_{k=1}^n 1 - 1_{A_k} = \sum_{I \subset \{1,2,...,n\} }(-1)^{card(I)}1_{A_I}$

Second exact sequence for closed embedding of nonsingular varieties.

In proving every open connected subset of $\mathbb{R}^n$ is path connected

IMO 2005 No 4. : All integers relatively prime to terms of infinite sequence

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