List questions from supremum-and-infimum

Published on 29 Mar 2018 - 14:20

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continuous function is bounded above and attains it's upper bound

Published on 29 Mar 2018 - 14:55

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Is convex function? (related to sup.)

Published on 30 Mar 2018 - 8:46

286

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$\sup${$\frac{\sin nx}{\sin x}:n\in\mathbb Z$}: Upper boundary of $\frac{\sin nx}{\sin x}$

Published on 22 Feb 2026 - 23:41

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Essential range of a continous function.

Published on 01 Apr 2018 - 17:43

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Show that any upper bounded subset of $\mathbb{Z}$ has a unique maximal element

Published on 01 Apr 2018 - 18:17

58

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Continuity of $x \mapsto \inf \left\{ || x - u || \mid u \in U \right\}$

Published on 01 Apr 2018 - 19:57

43

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Which definition of the least upper bound is right

Published on 25 Mar 2026 - 13:59

92

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How to show that $ \langle \sqrt n \rangle $ is not converging

Published on 25 Mar 2026 - 1:16

229

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Taking a supremum of an infimum (in a game theory context)

Published on 04 Apr 2018 - 10:24

36

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Supremum vs limit supremum; notation confusion

Published on 05 Apr 2018 - 1:00

132

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Can we establish the following inequalities

Published on 05 Apr 2018 - 4:18

60

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Is $f(t):=\inf\lbrace x : F(x,t)<\phi(t) \rbrace $ continuous?

Published on 05 Apr 2018 - 18:18

268

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Prove that the supremum of a set of nested square roots is 2

Published on 11 Apr 2018 - 11:06

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Proving that $\sup\limits_{n\geq 1}\{a_n+b_n\}\neq \sup\limits_{n\geq 1}a_n+\sup\limits_{n\geq 1}b_n$

Published on 11 Apr 2018 - 22:06

List Question

Supremum of absolute difference equals Sup - Inf

continuous function is bounded above and attains it's upper bound

Is convex function? (related to sup.)

$\sup${$\frac{\sin nx}{\sin x}:n\in\mathbb Z$}: Upper boundary of $\frac{\sin nx}{\sin x}$

Essential range of a continous function.

Show that any upper bounded subset of $\mathbb{Z}$ has a unique maximal element

Continuity of $x \mapsto \inf \left\{ || x - u || \mid u \in U \right\}$

Which definition of the least upper bound is right

How to show that $ \langle \sqrt n \rangle $ is not converging

Taking a supremum of an infimum (in a game theory context)

Supremum vs limit supremum; notation confusion

Can we establish the following inequalities

Is $f(t):=\inf\lbrace x : F(x,t)<\phi(t) \rbrace $ continuous?

Prove that the supremum of a set of nested square roots is 2

Proving that $\sup\limits_{n\geq 1}\{a_n+b_n\}\neq \sup\limits_{n\geq 1}a_n+\sup\limits_{n\geq 1}b_n$

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