Question

Can a subset of Natural numbers be uncountable?

score 335 · Answer 1 · 2026-04-12 11:35:41

335

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Can a subset of Natural numbers be uncountable?

Published on 12 Apr 2026 - 11:35

score 137 · Answer 2 · 2026-05-10 16:20:18

137

Views

Do there exist any subsets of $\mathbb{R}$ with positive measure but not of size continuum?

Published on 10 May 2026 - 16:20

score 1.9k · Answer 3 · 2026-05-11 02:45:33

1.9k

Views

Prove that a power series that is zero on a sequence that converges to zero is the zero function

Published on 11 May 2026 - 2:45

score 135 · Answer 4 · 2026-04-15 01:00:45

135

Views

Prove there is a subsequence of a sequence that converges to $y$

Published on 15 Apr 2026 - 1:00

score 2.6k · Answer 5 · 2026-04-16 21:24:28

2.6k

Views

True or false, prove or find a counterexample. If $\{x_n\}$ is a sequence such that $\{x_n^2\}$ converges, then $\{x_n\}$ converges

Published on 16 Apr 2026 - 21:24

score 123 · Answer 6 · 2026-05-07 16:51:33

123

Views

When does $\int \limits_{\Bbb R} f \chi_{A} \,d\lambda$ = $\lambda$($A$) hold?

Published on 07 May 2026 - 16:51

score 249 · Answer 7 · 2026-04-11 09:52:58

249

Views

How can I prove that $f(x)=\sum_{k=1}^{\infty}\frac{\{kx\}}{k^{2}}$ is continuous?

Published on 11 Apr 2026 - 9:52

score 47 · Answer 8 · 2026-04-16 18:24:48

If $\, f \in C \left[a,b\right]\, $ and $a< x_1< x_2 < b,\, $ prove $\, \exists \xi \in(a,b)\, $ s.t. $\, f(\xi) = \frac{f(x_1) + f(x_2)}{2}$

score 971 · Answer 9 · 2026-05-10 18:25:12

971

Views

Prove Outer Measure of $\mathbb R$

Published on 10 May 2026 - 18:25

score 44 · Answer 10 · 2026-04-11 01:09:13

44

Views

Why is any function here uniformly continuous?

Published on 11 Apr 2026 - 1:09

score 81 · Answer 11 · 2026-05-11 06:35:44

81

Views

What about an approximation of the Hölder's constant associated to $\sum_{n=0}^\infty\gamma^n\cos(11^n\pi x)$, where $\gamma$ is the Euler's constant?

Published on 11 May 2026 - 6:35

score 206 · Answer 12 · 2026-04-13 20:00:30

206

Views

every bijection is an homeomorphism

Published on 13 Apr 2026 - 20:00

score 434 · Answer 13 · 2026-04-15 22:41:28

434

Views

Prove that there exists an irrational number $\\a$ such that $x< au< y$ if $x< y$ and $u> 0$.

Published on 15 Apr 2026 - 22:41

score 1.5k · Answer 14 · 2026-04-10 12:43:48

1.5k

Views

General product rule formula for multivariable functions?

Published on 10 Apr 2026 - 12:43

score 57 · Answer 15 · 2026-05-12 23:40:30

57

Views

prove of two sets being equal

Published on 12 May 2026 - 23:40

List Question

Can a subset of Natural numbers be uncountable?

Do there exist any subsets of $\mathbb{R}$ with positive measure but not of size continuum?

Prove that a power series that is zero on a sequence that converges to zero is the zero function

Prove there is a subsequence of a sequence that converges to $y$

True or false, prove or find a counterexample. If $\{x_n\}$ is a sequence such that $\{x_n^2\}$ converges, then $\{x_n\}$ converges

When does $\int \limits_{\Bbb R} f \chi_{A} \,d\lambda$ = $\lambda$($A$) hold?

How can I prove that $f(x)=\sum_{k=1}^{\infty}\frac{\{kx\}}{k^{2}}$ is continuous?

If $\, f \in C \left[a,b\right]\, $ and $a< x_1< x_2 < b,\, $ prove $\, \exists \xi \in(a,b)\, $ s.t. $\, f(\xi) = \frac{f(x_1) + f(x_2)}{2}$

Prove Outer Measure of $\mathbb R$

Why is any function here uniformly continuous?

What about an approximation of the Hölder's constant associated to $\sum_{n=0}^\infty\gamma^n\cos(11^n\pi x)$, where $\gamma$ is the Euler's constant?

every bijection is an homeomorphism

Prove that there exists an irrational number $\\a$ such that $x< au< y$ if $x< y$ and $u> 0$.

General product rule formula for multivariable functions?

prove of two sets being equal

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