List questions from supremum-and-infimum

Published on 11 Feb 2016 - 6:35

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Determine supremum and infimum of $\{x \in \Bbb R\,:\, x < 3/x\}$

Published on 12 Feb 2016 - 14:37

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Proof verification: Compact set has sup and inf

Published on 13 Feb 2016 - 2:39

194

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Prove that $\liminf_{n\rightarrow\infty}s_n\leqslant \liminf_{n\rightarrow\infty}\sigma_n$ for $\sigma_n=n^{-1}(s_1+...+s_n)$.

Published on 03 Apr 2026 - 3:38

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Difference of Suprema

Published on 03 Apr 2026 - 0:48

6.9k

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To show that the supremum of any collection of lower semicontinuous functions is lower semicontinuous

Published on 23 Feb 2026 - 14:50

2.8k

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Prove sequence of continuous functions is Cauchy

Published on 03 Apr 2026 - 1:44

160

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Adherence values of a sequence

Published on 03 Apr 2026 - 5:24

48

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$A = \{f \in C[0,1]: |f(t)| < k(t), \forall t \in [0,1]\}$ - Show that $A$ is open

Published on 23 Feb 2016 - 3:41

997

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$ \sup_{x \in A}\log(f(x))=\log(\sup_{x \in A}f(x)) $?

Published on 29 Mar 2026 - 11:18

462

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Give an example where the inequalities are strict $\sup (\inf A,\inf B) \le \inf (A \cap B) \le \sup (A \cap B) \le \inf (\sup A, \sup B)$

Published on 28 Feb 2016 - 6:15

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proving existence of supremum in $\mathbb Q$

Published on 29 Feb 2016 - 6:33

3.1k

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When is a function of the largest eigenvalue continuous and/or differentiable?

Published on 01 Mar 2016 - 14:59

99

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Relationship between norm of a function and its supremum

Published on 01 Mar 2016 - 17:20

785

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maximum, supremum, and supremum norm

Published on 02 Mar 2016 - 14:53

List Question

Why is the sequence $u_N = \inf\{s_n : n \gt N\}$ increasing?

Determine supremum and infimum of $\{x \in \Bbb R\,:\, x < 3/x\}$

Proof verification: Compact set has sup and inf

Prove that $\liminf_{n\rightarrow\infty}s_n\leqslant \liminf_{n\rightarrow\infty}\sigma_n$ for $\sigma_n=n^{-1}(s_1+...+s_n)$.

Difference of Suprema

To show that the supremum of any collection of lower semicontinuous functions is lower semicontinuous

Prove sequence of continuous functions is Cauchy

Adherence values of a sequence

$A = \{f \in C[0,1]: |f(t)| < k(t), \forall t \in [0,1]\}$ - Show that $A$ is open

$ \sup_{x \in A}\log(f(x))=\log(\sup_{x \in A}f(x)) $?

Give an example where the inequalities are strict $\sup (\inf A,\inf B) \le \inf (A \cap B) \le \sup (A \cap B) \le \inf (\sup A, \sup B)$

proving existence of supremum in $\mathbb Q$

When is a function of the largest eigenvalue continuous and/or differentiable?

Relationship between norm of a function and its supremum

maximum, supremum, and supremum norm

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