List questions from supremum-and-infimum

Published on 17 Sep 2016 - 19:53

50

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Calculate the upper boundary of the given sum

Published on 18 Sep 2016 - 17:17

184

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Using Least Upper Bound Property to prove that $n>r$ for any $r\in \mathbb{R}$

Published on 19 Sep 2016 - 4:46

2.4k

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Limit is less than the supremum

Published on 19 Sep 2016 - 9:50

189

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Inner Product of Bounded Self Adjoint Linear Operator

Published on 27 Mar 2026 - 19:31

71

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Proof of one of the operations on Random Variables

Published on 22 Sep 2016 - 23:36

44

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Let $B(x) = \left\{b^t \ | \ t \in \mathbb{Q} ,\ x \in \mathbb{R} \land t \leq x \ \right\}$. Prove that $b^r = \sup B(r)$ if $r$ is rational.

Published on 26 Sep 2016 - 2:23

990

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Prove that the function is bounded: $f(x) = \frac{1}{x^{2}+1}$

Published on 26 Sep 2016 - 9:58

100

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Prove or disprove: The function is bounded: $f(n) = n + \frac{1}{n}$

Published on 26 Sep 2016 - 11:19

401

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Find the supremum and the infimum of $A$

Published on 26 Sep 2016 - 21:41

1k

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find the supremum and infimum of a set S

Published on 27 Sep 2016 - 20:18

63

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Prove that $\inf_{t>0}\frac{ω(t)}t=\lim_{t\to\infty}\frac{ω(t)}t$ if $ω:[0,\infty)\toℝ$ be bounded above on every finite interval and subadditive

Published on 29 Mar 2026 - 5:58

44

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For bounded $S\subseteq\Bbb{R}$, $\alpha = \sup(S)$. For all $\varepsilon>0$, $\exists x\in S$ s.t. $\alpha-\varepsilon< x\leq \alpha$.

Published on 29 Sep 2016 - 16:07

27

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find the sup of the following sequence

Published on 29 Sep 2016 - 21:14

3.4k

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Proving $\inf F = - \sup E$

Published on 30 Sep 2016 - 4:59

List Question

Proving $x+y =\sup\left\{ r+s: r,s \in \mathbb{Q}, r\leq x, s\leq y\right\}$

Calculate the upper boundary of the given sum

Using Least Upper Bound Property to prove that $n>r$ for any $r\in \mathbb{R}$

Limit is less than the supremum

Inner Product of Bounded Self Adjoint Linear Operator

Proof of one of the operations on Random Variables

Let $B(x) = \left\{b^t \ | \ t \in \mathbb{Q} ,\ x \in \mathbb{R} \land t \leq x \ \right\}$. Prove that $b^r = \sup B(r)$ if $r$ is rational.

Prove that the function is bounded: $f(x) = \frac{1}{x^{2}+1}$

Prove or disprove: The function is bounded: $f(n) = n + \frac{1}{n}$

Find the supremum and the infimum of $A$

find the supremum and infimum of a set S

Prove that $\inf_{t>0}\frac{ω(t)}t=\lim_{t\to\infty}\frac{ω(t)}t$ if $ω:[0,\infty)\toℝ$ be bounded above on every finite interval and subadditive

For bounded $S\subseteq\Bbb{R}$, $\alpha = \sup(S)$. For all $\varepsilon>0$, $\exists x\in S$ s.t. $\alpha-\varepsilon< x\leq \alpha$.

find the sup of the following sequence

Proving $\inf F = - \sup E$

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