Question

Show $\lim \dfrac{ a_n }{n} $ exists if $0 \leq a_{n+m} \leq a_n + a_m $

score 314 · Answer 1 · 2020-05-20 07:52:02

314

Views

Show $\lim \dfrac{ a_n }{n} $ exists if $0 \leq a_{n+m} \leq a_n + a_m $

Published on 20 May 2020 - 7:52

score 66 · Answer 2 · 2026-03-29 08:15:55

66

Views

Showing that for $x > e^{2.5102}, 0 \le \lfloor\dfrac{1.25506(x+1)}{\ln(x+1)}\rfloor - \lfloor\dfrac{1.25506x}{\ln x}\rfloor \le 1$

Published on 29 Mar 2026 - 8:15

score 2.1k · Answer 3 · 2026-04-12 19:09:57

2.1k

Views

If a function is continuous on a closed interval, then it is bounded on that interval.

Published on 12 Apr 2026 - 19:09

score 179 · Answer 4 · 2026-04-13 19:28:46

179

Views

Let $f:X\to Y$ be a map between first countable Hausdorff spaces s.t. $f^{-1}(K)$ is compact, for all compact $K\subset Y$. Show that $f$ is closed.

Published on 13 Apr 2026 - 19:28

score 122 · Answer 5 · 2026-04-13 18:20:34

Find the number of ways $v_n$ of seating $n$ couples around a rectangular table such that no one is allowed to sit across from his or her partner

score 63 · Answer 6 · 2026-04-11 06:10:19

63

Views

(Proof verification) there is no homomorphism between a finite field’s additive group to its multiplicative group.

Published on 11 Apr 2026 - 6:10

score 149 · Answer 7 · 2026-04-11 23:15:05

149

Views

Attempted Proof of Löwenheim-Skolem theorem

Published on 11 Apr 2026 - 23:15

score 136 · Answer 8 · 2026-03-30 15:14:55

136

Views

Solving $f(x^2 + y) = f(x^{27} + 2y) + f(x^4)$

Published on 30 Mar 2026 - 15:14

score 125 · Answer 9 · 2026-04-13 09:46:52

125

Views

Is it possible to evaluate $\iiint \frac{2x^2+z^2}{x^2+z^2} dxdydz$ using cylindrical coordinates instead of spherical?

Published on 13 Apr 2026 - 9:46

score 136 · Answer 10 · 2026-04-12 15:19:39

136

Views

Cauchy Product of two geometric series.

Published on 12 Apr 2026 - 15:19

score 140 · Answer 11 · 2026-04-11 04:54:39

140

Views

Not every compact subset of $\mathbb{R}$ is the support of a continuous function

Published on 11 Apr 2026 - 4:54

score 41 · Answer 12 · 2026-04-11 11:58:42

41

Views

Acceleration $\mathbf a$ in function of the velocity $\mathbf v$

Published on 11 Apr 2026 - 11:58

score 101 · Answer 13 · 2026-04-14 03:10:03

101

Views

Compute the integral of $e^{-x}$

Published on 14 Apr 2026 - 3:10

score 846 · Answer 14 · 2026-03-26 14:23:02

846

Views

Prove that a sequence $f_n$ of functions which are bounded and converges uniformly to $f$, which is also bounded, is uniformly bounded

Published on 26 Mar 2026 - 14:23

score 644 · Answer 15 · 2026-04-13 04:22:45

644

Views

Question on dice rolling -- expected number of rolls to get a particular sequence

Published on 13 Apr 2026 - 4:22

List Question

Show $\lim \dfrac{ a_n }{n} $ exists if $0 \leq a_{n+m} \leq a_n + a_m $

Showing that for $x > e^{2.5102}, 0 \le \lfloor\dfrac{1.25506(x+1)}{\ln(x+1)}\rfloor - \lfloor\dfrac{1.25506x}{\ln x}\rfloor \le 1$

If a function is continuous on a closed interval, then it is bounded on that interval.

Let $f:X\to Y$ be a map between first countable Hausdorff spaces s.t. $f^{-1}(K)$ is compact, for all compact $K\subset Y$. Show that $f$ is closed.

Find the number of ways $v_n$ of seating $n$ couples around a rectangular table such that no one is allowed to sit across from his or her partner

(Proof verification) there is no homomorphism between a finite field’s additive group to its multiplicative group.

Attempted Proof of Löwenheim-Skolem theorem

Solving $f(x^2 + y) = f(x^{27} + 2y) + f(x^4)$

Is it possible to evaluate $\iiint \frac{2x^2+z^2}{x^2+z^2} dxdydz$ using cylindrical coordinates instead of spherical?

Cauchy Product of two geometric series.

Not every compact subset of $\mathbb{R}$ is the support of a continuous function

Acceleration $\mathbf a$ in function of the velocity $\mathbf v$

Compute the integral of $e^{-x}$

Prove that a sequence $f_n$ of functions which are bounded and converges uniformly to $f$, which is also bounded, is uniformly bounded

Question on dice rolling -- expected number of rolls to get a particular sequence

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