List questions from supremum-and-infimum

Published on 09 Apr 2026 - 7:11

53

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How does the author obtain $\psi(\bar{y}) \neq \pm \infty$ in this theorem about $c$-cyclically monotone set?

Published on 24 Feb 2026 - 21:00

52

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The property of normed space, , closed subspace, and distance.

Published on 24 Jul 2022 - 5:24

369

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Prove that $b^x b^y = b^{x+y}$ for all real $x$ and $y$.

Published on 26 Jul 2022 - 11:16

198

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$l^p$ spaces are increasing in $p$

Published on 29 Jul 2022 - 16:30

64

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stronger variant of "$l^p$ spaces are increasing in $p$"： $\bigcup_{1\leq p\lneq q}l^p\neq l^q$

Published on 30 Jul 2022 - 0:37

58

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Proving that $\sup A = k - \inf B$ when $A,B$ are related by a map.

Published on 02 Aug 2022 - 13:59

383

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Proof that $\sup(c+A) = c + \sup(A)$

Published on 06 Aug 2022 - 15:48

30

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In general what are the min and max values of $(x)_{\pmod d} - \dfrac{(x)_{\pmod {2d}}}{2}$?

Published on 08 Aug 2022 - 9:08

421

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Supremum of set union

Published on 09 Aug 2022 - 15:18

96

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Confusion about the least upper bound property

Published on 13 Aug 2022 - 18:17

156

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Question about the Legendre transform

Published on 23 Feb 2026 - 22:17

69

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Proof verification: If $A$ is an ordered set with the least upper bound property, then $A$ also has the greatest lower bound property.

Published on 18 Aug 2022 - 6:58

87

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An equality about an infimum over a vector: $\inf_y = \inf_{\|v\|=1}\inf_t$

Published on 19 Aug 2022 - 18:16

303

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Definition of supremum clarification (Abbott - Understanding Analysis Lemma 1.3.8)

Published on 24 Aug 2022 - 20:58

List Question

The measurability of $c$-transform

How does the author obtain $\psi(\bar{y}) \neq \pm \infty$ in this theorem about $c$-cyclically monotone set?

The property of normed space, , closed subspace, and distance.

Prove that $b^x b^y = b^{x+y}$ for all real $x$ and $y$.

$l^p$ spaces are increasing in $p$

stronger variant of "$l^p$ spaces are increasing in $p$"： $\bigcup_{1\leq p\lneq q}l^p\neq l^q$

Proving that $\sup A = k - \inf B$ when $A,B$ are related by a map.

Proof that $\sup(c+A) = c + \sup(A)$

In general what are the min and max values of $(x)_{\pmod d} - \dfrac{(x)_{\pmod {2d}}}{2}$?

Supremum of set union

Confusion about the least upper bound property

Question about the Legendre transform

Proof verification: If $A$ is an ordered set with the least upper bound property, then $A$ also has the greatest lower bound property.

An equality about an infimum over a vector: $\inf_y = \inf_{\|v\|=1}\inf_t$

Definition of supremum clarification (Abbott - Understanding Analysis Lemma 1.3.8)

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