Question

prove $|X-Y|\le|X|+|Y|$

score 525 · Answer 1 · 2026-05-10 18:01:37

525

Views

prove $|X-Y|\le|X|+|Y|$

Published on 10 May 2026 - 18:01

score 238 · Answer 2 · 2026-04-13 17:03:13

238

Views

Proving an arbitrary set is open

Published on 13 Apr 2026 - 17:03

score 51 · Answer 3 · 2026-04-14 00:10:14

51

Views

Dose $F' > 0$ imply $F$ is stirctly increasing?

Published on 14 Apr 2026 - 0:10

score 114 · Answer 4 · 2026-04-18 18:14:56

114

Views

Solving three alike problems $a_{n+1} = \frac{1+a_n^2}{1+a_n}$

Published on 18 Apr 2026 - 18:14

score 298 · Answer 5 · 2026-04-16 15:26:38

Why is my proof wrong? (Rudin Ch 3 #8) If $\sum a_n$ converges, and if ${b_n}$ is monotonic and bounded, prove that $\sum a_n b_n$ converges.

score 88 · Answer 6 · 2026-04-15 08:13:48

$f(x)$ is positive and integrable on $[a,b]$. Does that imply $\int _a^x f(t)dt$ is positive for $x\in (a,b]$?

score 351 · Answer 7 · 2026-04-08 09:18:50

351

Views

Proof of equivalence between open-set and $\varepsilon$-$\delta$ definition of continuity.

Published on 08 Apr 2026 - 9:18

score 369 · Answer 8 · 2026-04-13 20:22:26

Real Analysis. Is my proof okay? Show that the Cantor set is totally disconnected in R, i.e. it contains no subset that is connected.

score 1.7k · Answer 9 · 2026-05-14 17:08:25

1.7k

Views

Open Sets and Sequence Convergence

Published on 14 May 2026 - 17:08

score 119 · Answer 10 · 2026-05-13 18:31:18

119

Views

A non-smooth map with smooth Jacobian?

Published on 13 May 2026 - 18:31

score 183 · Answer 11 · 2026-05-10 21:52:18

183

Views

Showing a Sequence Converges to Sup $F$

Published on 10 May 2026 - 21:52

score 148 · Answer 12 · 2026-04-14 20:23:39

148

Views

Convergence in $L^2$ implies uniform convergence for the normalized functions

Published on 14 Apr 2026 - 20:23

score 107 · Answer 13 · 2026-04-14 11:12:33

107

Views

What does the indicator function $\mathbb{1}_A:S\to\mathbb{R}$ do?

Published on 14 Apr 2026 - 11:12

score 2.9k · Answer 14 · 2026-05-10 18:30:28

2.9k

Views

If $f:[a,b]\to R$ is bounded with points of discontinuities enclosed by finite number of sub-intervals then $f$ is Riemann integrable on $[a,b]$.

Published on 10 May 2026 - 18:30

score 46 · Answer 15 · 2026-04-18 18:33:02

46

Views

How $\lim_{n\to\infty}\frac{|x|}{(1+x^{2n})^{\frac{1}{n}}}=\frac{1}{|x|}\lim_{n\to\infty}\frac{1}{(1+\frac{1}{2^n})^{\frac{1}{n}}}$?

Published on 18 Apr 2026 - 18:33

List Question

prove $|X-Y|\le|X|+|Y|$

Proving an arbitrary set is open

Dose $F' > 0$ imply $F$ is stirctly increasing?

Solving three alike problems $a_{n+1} = \frac{1+a_n^2}{1+a_n}$

Why is my proof wrong? (Rudin Ch 3 #8) If $\sum a_n$ converges, and if ${b_n}$ is monotonic and bounded, prove that $\sum a_n b_n$ converges.

$f(x)$ is positive and integrable on $[a,b]$. Does that imply $\int _a^x f(t)dt$ is positive for $x\in (a,b]$?

Proof of equivalence between open-set and $\varepsilon$-$\delta$ definition of continuity.

Real Analysis. Is my proof okay? Show that the Cantor set is totally disconnected in R, i.e. it contains no subset that is connected.

Open Sets and Sequence Convergence

A non-smooth map with smooth Jacobian?

Showing a Sequence Converges to Sup $F$

Convergence in $L^2$ implies uniform convergence for the normalized functions

What does the indicator function $\mathbb{1}_A:S\to\mathbb{R}$ do?

If $f:[a,b]\to R$ is bounded with points of discontinuities enclosed by finite number of sub-intervals then $f$ is Riemann integrable on $[a,b]$.

How $\lim_{n\to\infty}\frac{|x|}{(1+x^{2n})^{\frac{1}{n}}}=\frac{1}{|x|}\lim_{n\to\infty}\frac{1}{(1+\frac{1}{2^n})^{\frac{1}{n}}}$?

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