Question

Let $f:[0,1] \to \mathbf {R}$, continuous and $f(0)=f(1)$. Prove $f(x)=f(x+\frac{1}{2})$ has a solution $x_0 \in [0,\frac{1}{2}]$

score 61 · Answer 1 · 2026-04-16 10:08:53

61

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Let $f:[0,1] \to \mathbf {R}$, continuous and $f(0)=f(1)$. Prove $f(x)=f(x+\frac{1}{2})$ has a solution $x_0 \in [0,\frac{1}{2}]$

Published on 16 Apr 2026 - 10:08

score 38 · Answer 2 · 2026-04-12 01:56:34

38

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Question on proof of power sets

Published on 12 Apr 2026 - 1:56

score 92 · Answer 3 · 2026-04-13 03:15:26

92

Views

Uniform convergence of heat kernel

Published on 13 Apr 2026 - 3:15

score 108 · Answer 4 · 2026-04-15 21:21:37

108

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Proving there is one group of order $3$, up to isomorphism

Published on 15 Apr 2026 - 21:21

score 71 · Answer 5 · 2026-04-14 15:25:51

71

Views

Uniform convergence of the Laplacian of heat kernel

Published on 14 Apr 2026 - 15:25

score 43 · Answer 6 · 2026-04-16 06:07:47

43

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If $x,\overline{x}$ are non-real complex numbers, then if $x,\overline{x}$ solves $z^2+az+b=0$ then $a,b\in \mathbb{R}$

Published on 16 Apr 2026 - 6:07

score 68 · Answer 7 · 2026-04-14 07:59:17

68

Views

Volume of the solid of revolution: $y=x^2$ about $y=x$.

Published on 14 Apr 2026 - 7:59

score 67 · Answer 8 · 2026-04-14 02:43:27

67

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Computing the tangent plane of a surface $f(x,y,z)=0$

Published on 14 Apr 2026 - 2:43

score 73 · Answer 9 · 2026-04-16 07:54:06

73

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Given $g(x)$ is continuous and $\int_0^a g(x)dx = 0$, $\forall a\geq0$, prove that $g(x)=0$, $\forall x \geq0$. Proof without using FTC?

Published on 16 Apr 2026 - 7:54

score 24 · Answer 10 · 2026-04-17 06:46:42

24

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How to prove that when $ac ≡ bc (mod \space m)$, and $GCD(c, m) = 1$, then $a ≡ b (mod \space m)$?

Published on 17 Apr 2026 - 6:46

score 41 · Answer 11 · 2026-04-15 19:55:31

41

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In $(X,S,\mu), \int f^r d\mu<\infty\implies \int f^q d\mu<\infty$, where $\mu(X)<\infty$.

Published on 15 Apr 2026 - 19:55

score 67 · Answer 12 · 2026-04-09 11:29:51

67

Views

Sufficient conditions for series to converge in Banach spaces

Published on 09 Apr 2026 - 11:29

score 45 · Answer 13 · 2026-04-12 19:11:03

45

Views

Ambiguous probability problem

Published on 12 Apr 2026 - 19:11

score 78 · Answer 14 · 2026-04-15 03:48:51

78

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Multivariable calculus: strict local minimum of $f(x,y) = y^2 - 3x^2y+2x^4$

Published on 15 Apr 2026 - 3:48

score 54 · Answer 15 · 2026-04-13 08:57:00

54

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Equality in $\mathbb{Z}$ versus equality in $\mathbb{Q}$

Published on 13 Apr 2026 - 8:57

List Question

Let $f:[0,1] \to \mathbf {R}$, continuous and $f(0)=f(1)$. Prove $f(x)=f(x+\frac{1}{2})$ has a solution $x_0 \in [0,\frac{1}{2}]$

Question on proof of power sets

Uniform convergence of heat kernel

Proving there is one group of order $3$, up to isomorphism

Uniform convergence of the Laplacian of heat kernel

If $x,\overline{x}$ are non-real complex numbers, then if $x,\overline{x}$ solves $z^2+az+b=0$ then $a,b\in \mathbb{R}$

Volume of the solid of revolution: $y=x^2$ about $y=x$.

Computing the tangent plane of a surface $f(x,y,z)=0$

Given $g(x)$ is continuous and $\int_0^a g(x)dx = 0$, $\forall a\geq0$, prove that $g(x)=0$, $\forall x \geq0$. Proof without using FTC?

How to prove that when $ac ≡ bc (mod \space m)$, and $GCD(c, m) = 1$, then $a ≡ b (mod \space m)$?

In $(X,S,\mu), \int f^r d\mu<\infty\implies \int f^q d\mu<\infty$, where $\mu(X)<\infty$.

Sufficient conditions for series to converge in Banach spaces

Ambiguous probability problem

Multivariable calculus: strict local minimum of $f(x,y) = y^2 - 3x^2y+2x^4$

Equality in $\mathbb{Z}$ versus equality in $\mathbb{Q}$

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