Question

Prove that $\sup(S)\leq\sup(T)$ and $\inf(T)\leq\inf(S)$

score 2.1k · Answer 1 · 2026-04-14 21:55:02

2.1k

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Prove that $\sup(S)\leq\sup(T)$ and $\inf(T)\leq\inf(S)$

Published on 14 Apr 2026 - 21:55

score 138 · Answer 2 · 2026-05-11 04:59:58

138

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Tips/Tricks for beginners in Analysis and Recommendation

Published on 11 May 2026 - 4:59

score 49 · Answer 3 · 2026-04-11 08:49:02

49

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Limit of big O term.

Published on 11 Apr 2026 - 8:49

score 741 · Answer 4 · 2026-04-15 15:45:31

741

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Show that $\sup(S)=\inf(T)$.

Published on 15 Apr 2026 - 15:45

score 72 · Answer 5 · 2026-05-10 16:35:47

72

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Prove $\exists \alpha \in ]0,1]$ such as : $|F(x)-F(y)| \leq ||f||_p |x-y|^{\alpha}$ (Holder)

Published on 10 May 2026 - 16:35

score 116 · Answer 6 · 2026-04-15 04:44:03

116

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Prove that $S$ is a finite set.

Published on 15 Apr 2026 - 4:44

score 104 · Answer 7 · 2026-04-16 02:55:11

104

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Construct $(y_n)$ such that $x_n \leq y_n \leq 2y_{f(n)}$ where $f:\mathbb{N}_{\geq 0} \to \mathbb{N}_{\geq 1}$ is strictly increasing

Published on 16 Apr 2026 - 2:55

score 47 · Answer 8 · 2026-05-10 19:00:25

Take $f:\mathbb{R}\rightarrow\mathbb{R}$ and for each $r\in \mathbb{R}$ collect $f(r)$ in $\mathcal{A}_f$: what is $\mathcal{A}_f$?

score 48 · Answer 9 · 2026-05-15 05:27:31

48

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Continuous function composition

Published on 15 May 2026 - 5:27

score 41 · Answer 10 · 2026-04-13 04:24:05

41

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Differentiability of $ -f$

Published on 13 Apr 2026 - 4:24

score 33 · Answer 11 · 2026-04-16 06:36:30

33

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Series convergence for every real number

Published on 16 Apr 2026 - 6:36

score 2.6k · Answer 12 · 2026-04-15 00:00:53

2.6k

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Show that $f'(x) = f^2(x)$ and $f(0) = 0$ implies $f$ is the zero function

Published on 15 Apr 2026 - 0:00

score 72 · Answer 13 · 2026-04-13 21:11:32

72

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How to solve for $x$ in $(16)^\frac{1}{x} = \frac{10}{3}$

Published on 13 Apr 2026 - 21:11

score 30 · Answer 14 · 2026-04-13 14:04:41

30

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Suppose the total cost, TC, is the sum of two parts of costs

Published on 13 Apr 2026 - 14:04

score 56 · Answer 15 · 2026-04-25 00:16:02

56

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One Estimate about $\int_{\mathbb{R}^n} \frac{g(x+z)f(x+z)-g(x)f(x)- \mathbf{1}_{|z|<1}\nabla g(x)f(x)\cdot z}{|z|^{n+2s}}dz$

Published on 25 Apr 2026 - 0:16

List Question

Prove that $\sup(S)\leq\sup(T)$ and $\inf(T)\leq\inf(S)$

Tips/Tricks for beginners in Analysis and Recommendation

Limit of big O term.

Show that $\sup(S)=\inf(T)$.

Prove $\exists \alpha \in ]0,1]$ such as : $|F(x)-F(y)| \leq ||f||_p |x-y|^{\alpha}$ (Holder)

Prove that $S$ is a finite set.

Construct $(y_n)$ such that $x_n \leq y_n \leq 2y_{f(n)}$ where $f:\mathbb{N}_{\geq 0} \to \mathbb{N}_{\geq 1}$ is strictly increasing

Take $f:\mathbb{R}\rightarrow\mathbb{R}$ and for each $r\in \mathbb{R}$ collect $f(r)$ in $\mathcal{A}_f$: what is $\mathcal{A}_f$?

Continuous function composition

Differentiability of $ -f$

Series convergence for every real number

Show that $f'(x) = f^2(x)$ and $f(0) = 0$ implies $f$ is the zero function

How to solve for $x$ in $(16)^\frac{1}{x} = \frac{10}{3}$

Suppose the total cost, TC, is the sum of two parts of costs

One Estimate about $\int_{\mathbb{R}^n} \frac{g(x+z)f(x+z)-g(x)f(x)- \mathbf{1}_{|z|<1}\nabla g(x)f(x)\cdot z}{|z|^{n+2s}}dz$

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