Question

Show that given conditions, the given distance function is not a metric

score 31 · Answer 1 · 2026-04-14 07:19:12

31

Views

Show that given conditions, the given distance function is not a metric

Published on 14 Apr 2026 - 7:19

score 56 · Answer 2 · 2026-04-13 22:49:16

56

Views

Show that $f$ is injective in $(a,b)$

Published on 13 Apr 2026 - 22:49

score 57 · Answer 3 · 2026-05-14 19:39:56

57

Views

Does there exist a metric on $\mathbb{R}$ for which any $x$ is between any $y$ and $z$?

Published on 14 May 2026 - 19:39

score 69 · Answer 4 · 2026-04-13 19:58:51

69

Views

Suppose that $f$ is continuous and $h\neq 0$. Let $D_hf(x)=\frac{3}{2h^3}\int_{-h}^{h}tf(x+t)dt$. (a) Show that $D_hp(x)=p'(x)$ for all polynomials

Published on 13 Apr 2026 - 19:58

score 113 · Answer 5 · 2026-05-15 07:41:43

113

Views

Show that the set of non-$\beta$-Hölder functions is dense in the space of $\alpha$-Hölder function, $0<\alpha<\beta<1$

Published on 15 May 2026 - 7:41

score 60 · Answer 6 · 2026-05-10 20:43:58

60

Views

Find $\sup\{f(x)|x\in [\frac{r-1}{n}, \frac{r}{n}]\cap Q^c\}$

Published on 10 May 2026 - 20:43

score 71 · Answer 7 · 2026-04-15 23:20:16

71

Views

Prove $\bigcap_{n\in\mathbb N}[n,\infty)\ne\varnothing$

Published on 15 Apr 2026 - 23:20

score 45 · Answer 8 · 2026-04-16 07:26:26

45

Views

Proof verification: Why we can find $S\subset S_{\sigma_0}$ such that $\mu(S)>0$?

Published on 16 Apr 2026 - 7:26

score 848 · Answer 9 · 2026-05-16 00:19:45

848

Views

Is it a jointly concave function of $(x,y,z)$?

Published on 16 May 2026 - 0:19

score 168 · Answer 10 · 2026-04-16 05:41:47

168

Views

Prove that the infinite intersection of $R_n = [0,\frac{1}{n}] \times [0,\frac{1}{2n}]$ equals $(0,0)$

Published on 16 Apr 2026 - 5:41

score 160 · Answer 11 · 2026-04-11 19:07:00

160

Views

Does $n^2-\sin(n)\sqrt{n}$ go to $+\infty$ as $n \to +\infty$?

Published on 11 Apr 2026 - 19:07

score 48 · Answer 12 · 2026-04-19 04:22:15

48

Views

Understanding a limit on $R^n$ in a more rigorous way

Published on 19 Apr 2026 - 4:22

score 55 · Answer 13 · 2026-05-11 08:23:50

55

Views

Which function or sequence of functions if we integrate it becomes a constant?

Published on 11 May 2026 - 8:23

score 308 · Answer 14 · 2026-04-19 12:09:35

308

Views

Prove that $\lim_{n\to\infty} 1/n^\alpha = 0$ for any $\alpha > 0$.

Published on 19 Apr 2026 - 12:09

score 153 · Answer 15 · 2026-04-15 07:18:14

153

Views

What is value of limit $\lim_{n\to \infty}\frac{(2n)!}{4^n(n!)^2}$

Published on 15 Apr 2026 - 7:18

List Question

Show that given conditions, the given distance function is not a metric

Show that $f$ is injective in $(a,b)$

Does there exist a metric on $\mathbb{R}$ for which any $x$ is between any $y$ and $z$?

Suppose that $f$ is continuous and $h\neq 0$. Let $D_hf(x)=\frac{3}{2h^3}\int_{-h}^{h}tf(x+t)dt$. (a) Show that $D_hp(x)=p'(x)$ for all polynomials

Show that the set of non-$\beta$-Hölder functions is dense in the space of $\alpha$-Hölder function, $0<\alpha<\beta<1$

Find $\sup\{f(x)|x\in [\frac{r-1}{n}, \frac{r}{n}]\cap Q^c\}$

Prove $\bigcap_{n\in\mathbb N}[n,\infty)\ne\varnothing$

Proof verification: Why we can find $S\subset S_{\sigma_0}$ such that $\mu(S)>0$?

Is it a jointly concave function of $(x,y,z)$?

Prove that the infinite intersection of $R_n = [0,\frac{1}{n}] \times [0,\frac{1}{2n}]$ equals $(0,0)$

Does $n^2-\sin(n)\sqrt{n}$ go to $+\infty$ as $n \to +\infty$?

Understanding a limit on $R^n$ in a more rigorous way

Which function or sequence of functions if we integrate it becomes a constant?

Prove that $\lim_{n\to\infty} 1/n^\alpha = 0$ for any $\alpha > 0$.

What is value of limit $\lim_{n\to \infty}\frac{(2n)!}{4^n(n!)^2}$

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