Question

Prove that $\bigcap\limits^{\infty}_{n=1} \left(0, \frac{1}{n} \right)= \emptyset$

score 1.4k · Answer 1 · 2026-04-16 13:12:17

Prove that $\bigcap\limits^{\infty}_{n=1} \left(0, \frac{1}{n} \right)= \emptyset$

Published on 16 Apr 2026 - 13:12

score 50 · Answer 2 · 2026-04-16 17:25:04

Show that if $\lim\limits_{j \to \infty} b_j = \beta$ and $\beta < 0$ then $\exists$ $ N > \mathbb{N} $ such that j > N $\Rightarrow$ $b_j < 0 $.

score 114 · Answer 3 · 2026-04-17 07:19:04

114

Views

If $\int_a^b g(x)dx = 0$, then $g(x) = 0$ for a.e. $x$

Published on 17 Apr 2026 - 7:19

score 222 · Answer 4 · 2026-04-10 23:20:01

222

Views

Borel set with constant positive but not full measure in each interval.

Published on 10 Apr 2026 - 23:20

score 42 · Answer 5 · 2026-04-12 19:28:09

42

Views

Prove the continuity of a correspondence

Published on 12 Apr 2026 - 19:28

score 46 · Answer 6 · 2026-04-10 18:07:19

46

Views

domain of algebraic function

Published on 10 Apr 2026 - 18:07

score 1.8k · Answer 7 · 2026-04-16 04:02:17

1.8k

Views

Rudin 2.43 Every nonempty perfect set in $\mathbb{R}^k$ is uncountable

Published on 16 Apr 2026 - 4:02

score 81 · Answer 8 · 2026-04-13 10:03:52

81

Views

Where does the (2D) Hilbert curve map a given point to?

Published on 13 Apr 2026 - 10:03

score 187 · Answer 9 · 2026-04-16 14:10:51

187

Views

How to prove that $\int_{0}^{\pi}\left|{\sin{nx}\over x}\right|\,\mathrm dx\ge{2\over\pi} \sum\limits_{k = 1}^n \frac1k$

Published on 16 Apr 2026 - 14:10

score 63 · Answer 10 · 2026-04-16 16:44:27

63

Views

How to prove that $\exists c_1,c_2>0, F(t)\geq c_1 |t|^{\theta}-c_2$?

Published on 16 Apr 2026 - 16:44

score 57 · Answer 11 · 2026-04-13 23:47:59

57

Views

Show that the limit of a series is 0

Published on 13 Apr 2026 - 23:47

score 81 · Answer 12 · 2026-04-29 12:27:26

81

Views

Calculate $\int_{\mathbb R^3} x_3^2 e^{-\lVert x \rVert _2} \lambda_3(dx)$

Published on 29 Apr 2026 - 12:27

score 88 · Answer 13 · 2026-04-29 12:27:25

88

Views

Estimate on the integral

Published on 29 Apr 2026 - 12:27

score 276 · Answer 14 · 2026-04-11 20:11:45

276

Views

Do the terms of an infinite series constitute a countable set?

Published on 11 Apr 2026 - 20:11

score 60 · Answer 15 · 2026-04-15 11:38:17

60

Views

Taylor series of function with Lagrange Remainder

Published on 15 Apr 2026 - 11:38

List Question

Prove that $\bigcap\limits^{\infty}_{n=1} \left(0, \frac{1}{n} \right)= \emptyset$

Show that if $\lim\limits_{j \to \infty} b_j = \beta$ and $\beta < 0$ then $\exists$ $ N > \mathbb{N} $ such that j > N $\Rightarrow$ $b_j < 0 $.

If $\int_a^b g(x)dx = 0$, then $g(x) = 0$ for a.e. $x$

Borel set with constant positive but not full measure in each interval.

Prove the continuity of a correspondence

domain of algebraic function

Rudin 2.43 Every nonempty perfect set in $\mathbb{R}^k$ is uncountable

Where does the (2D) Hilbert curve map a given point to?

How to prove that $\int_{0}^{\pi}\left|{\sin{nx}\over x}\right|\,\mathrm dx\ge{2\over\pi} \sum\limits_{k = 1}^n \frac1k$

How to prove that $\exists c_1,c_2>0, F(t)\geq c_1 |t|^{\theta}-c_2$?

Show that the limit of a series is 0

Calculate $\int_{\mathbb R^3} x_3^2 e^{-\lVert x \rVert _2} \lambda_3(dx)$

Estimate on the integral

Do the terms of an infinite series constitute a countable set?

Taylor series of function with Lagrange Remainder

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