List questions from upper-lower-bounds

Published on 13 Feb 2021 - 11:34

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Prove the existence of $n\in\mathbb{N}$ such that $0<1/n<\epsilon$

Published on 31 Mar 2026 - 7:53

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Prove that for any $x\in\mathbb{R}$, there exists $k\in\mathbb{Z}$ such that $k\leq x$.

Published on 13 Feb 2021 - 23:26

90

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$l_1$ distance between $n$th fold product distributions $p^n$ and $q^n$

Published on 14 Feb 2021 - 7:33

196

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Bounding the difference between consecutive terms in the sequence $a_n=(1+1/n)^n$

Published on 14 Feb 2021 - 20:03

48

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Gaussian Mean Testing

Published on 24 Feb 2026 - 5:04

95

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Bounds on the AM-GM gap?

Published on 01 Apr 2026 - 13:16

2k

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Uniformly continuous function on bounded open interval is bounded

Published on 04 Apr 2026 - 15:13

179

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Confusion on Spivak's proof chapter 7-12

Published on 16 Feb 2021 - 0:12

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On the inequality $\frac{\sigma(n^2)}{q^k} < \frac{n^2 - q^k}{C}$ where $C>1$ and $q^k n^2$ is an odd perfect number - Part II

Published on 27 Mar 2026 - 13:10

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Easier proof of Hasse-Weil bound?

Published on 16 Feb 2021 - 17:43

156

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Convergence of $\sum_{n=0}^{\infty}a_nb_n$ if $a_n>0 \ \forall n\in \mathbf{N}$, $\sum_{n=0}^{\infty}a_n$ converges and $b_n$ bounded

Published on 16 Feb 2021 - 19:16

70

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If $\sum_{k=1}^{N}a_k$ bounded and $(b_k)$ is decreasing with $\lim_{k\to \infty}b_k=0$, then $\sum_{k=0}^{\infty}a_kb_k$ converges

Published on 16 Feb 2021 - 20:22

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Prove that the least upper bound of $A$ cannot be rational

Published on 17 Feb 2021 - 22:57

63

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On Perron's formula with remainder

Published on 22 Feb 2021 - 6:36

List Question

Prove that $\sqrt2$ is the least upper bound

Prove the existence of $n\in\mathbb{N}$ such that $0<1/n<\epsilon$

Prove that for any $x\in\mathbb{R}$, there exists $k\in\mathbb{Z}$ such that $k\leq x$.

$l_1$ distance between $n$th fold product distributions $p^n$ and $q^n$

Bounding the difference between consecutive terms in the sequence $a_n=(1+1/n)^n$

Gaussian Mean Testing

Bounds on the AM-GM gap?

Uniformly continuous function on bounded open interval is bounded

Confusion on Spivak's proof chapter 7-12

On the inequality $\frac{\sigma(n^2)}{q^k} < \frac{n^2 - q^k}{C}$ where $C>1$ and $q^k n^2$ is an odd perfect number - Part II

Easier proof of Hasse-Weil bound?

Convergence of $\sum_{n=0}^{\infty}a_nb_n$ if $a_n>0 \ \forall n\in \mathbf{N}$, $\sum_{n=0}^{\infty}a_n$ converges and $b_n$ bounded

If $\sum_{k=1}^{N}a_k$ bounded and $(b_k)$ is decreasing with $\lim_{k\to \infty}b_k=0$, then $\sum_{k=0}^{\infty}a_kb_k$ converges

Prove that the least upper bound of $A$ cannot be rational

On Perron's formula with remainder

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