Question

I cannot follow the logic of the proof of 3-5 Theorem on p.51 in "Calculus on Manifolds" by Michael Spivak. Please explain me.

score 63 · Answer 1 · 2026-04-14 14:20:56

63

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I cannot follow the logic of the proof of 3-5 Theorem on p.51 in "Calculus on Manifolds" by Michael Spivak. Please explain me.

Published on 14 Apr 2026 - 14:20

score 160 · Answer 2 · 2026-04-17 15:18:00

For $\pi<\alpha<\frac{3\pi}{2}$ what is the value of $\sqrt{4\sin^4\alpha + \sin^2 2\alpha} + 4\cos^2\left(\frac{\pi}{4} - \frac{\alpha}{2}\right)$?

score 138 · Answer 3 · 2026-04-10 14:08:23

138

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Is there a prime ideal of $gl_n$

Published on 10 Apr 2026 - 14:08

score 327 · Answer 4 · 2026-04-11 02:47:40

327

Views

Rudin Chapter 1, Exercise 20: new identity element for Dedekind cuts

Published on 11 Apr 2026 - 2:47

score 244 · Answer 5 · 2026-04-24 02:13:59

244

Views

Explaining a step in the proof of the Galois group of the composite field of two Galois fields with trivial intersection

Published on 24 Apr 2026 - 2:13

score 120 · Answer 6 · 2026-04-10 22:14:02

120

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China $1996$ Number theory Problem

Published on 10 Apr 2026 - 22:14

score 1.1k · Answer 7 · 2026-04-15 01:38:02

1.1k

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For $A, B \subset \mathbb{R}^+$, $\sup(A \cdot B) = \sup A \sup B$.

Published on 15 Apr 2026 - 1:38

score 76 · Answer 8 · 2026-04-14 22:27:12

76

Views

Why has this variable been used in Spivak's proof for Intermediate Value Theorem?

Published on 14 Apr 2026 - 22:27

score 239 · Answer 9 · 2026-03-27 23:48:15

239

Views

the Cartan subalgebra and a argument of the sum of two diagonalizable endomorphisms

Published on 27 Mar 2026 - 23:48

score 46 · Answer 10 · 2026-04-17 15:33:30

46

Views

Writing complex number $c$ in form $e^{iz}$

Published on 17 Apr 2026 - 15:33

score 88 · Answer 11 · 2026-04-08 21:02:00

88

Views

Question about the proof in Rudin's Real and Complex Analysis

Published on 08 Apr 2026 - 21:02

score 246 · Answer 12 · 2026-04-17 02:43:58

246

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Prove that $|AUC| = |A|$, where $A$ is an uncountable set and $C$ is a countable set.

Published on 17 Apr 2026 - 2:43

score 205 · Answer 13 · 2026-04-14 18:38:10

205

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How to prove that the area of quadrilateral $EHFG$ is equal to the sum of the areas of triangles $AGB$ and $DHC$?

Published on 14 Apr 2026 - 18:38

score 152 · Answer 14 · 2026-04-11 04:25:02

152

Views

Explaination of proof of Property of cyclic subgroup.

Published on 11 Apr 2026 - 4:25

score 295 · Answer 15 · 2026-04-15 11:36:42

295

Views

Construction of a bijection between set T of infinite binary strings and R

Published on 15 Apr 2026 - 11:36

List Question

I cannot follow the logic of the proof of 3-5 Theorem on p.51 in "Calculus on Manifolds" by Michael Spivak. Please explain me.

For $\pi<\alpha<\frac{3\pi}{2}$ what is the value of $\sqrt{4\sin^4\alpha + \sin^2 2\alpha} + 4\cos^2\left(\frac{\pi}{4} - \frac{\alpha}{2}\right)$?

Is there a prime ideal of $gl_n$

Rudin Chapter 1, Exercise 20: new identity element for Dedekind cuts

Explaining a step in the proof of the Galois group of the composite field of two Galois fields with trivial intersection

China $1996$ Number theory Problem

For $A, B \subset \mathbb{R}^+$, $\sup(A \cdot B) = \sup A \sup B$.

Why has this variable been used in Spivak's proof for Intermediate Value Theorem?

the Cartan subalgebra and a argument of the sum of two diagonalizable endomorphisms

Writing complex number $c$ in form $e^{iz}$

Question about the proof in Rudin's Real and Complex Analysis

Prove that $|AUC| = |A|$, where $A$ is an uncountable set and $C$ is a countable set.

How to prove that the area of quadrilateral $EHFG$ is equal to the sum of the areas of triangles $AGB$ and $DHC$?

Explaination of proof of Property of cyclic subgroup.

Construction of a bijection between set T of infinite binary strings and R

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