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Supremum of absolute difference equals Sup - Inf

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#real-analysis #proof-verification #supremum-and-infimum
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continuous function is bounded above and attains it's upper bound

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Is convex function? (related to sup.)

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#convex-optimization #supremum-and-infimum
290
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$\sup${$\frac{\sin nx}{\sin x}:n\in\mathbb Z$}: Upper boundary of $\frac{\sin nx}{\sin x}$

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#real-analysis #trigonometry #supremum-and-infimum #sequence-of-function
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Essential range of a continous function.

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#real-analysis #functional-analysis #measure-theory #supremum-and-infimum
888
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Show that any upper bounded subset of $\mathbb{Z}$ has a unique maximal element

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#real-analysis #supremum-and-infimum
61
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Continuity of $x \mapsto \inf \left\{ || x - u || \mid u \in U \right\}$

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#proof-verification #continuity #normed-spaces #supremum-and-infimum
46
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Which definition of the least upper bound is right

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#supremum-and-infimum #upper-lower-bounds
95
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How to show that $ \langle \sqrt n \rangle $ is not converging

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#calculus #sequences-and-series #supremum-and-infimum #natural-numbers
232
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Taking a supremum of an infimum (in a game theory context)

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#game-theory #supremum-and-infimum
39
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Supremum vs limit supremum; notation confusion

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#limits #notation #supremum-and-infimum
135
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Can we establish the following inequalities

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#inequality #supremum-and-infimum
63
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Is $f(t):=\inf\lbrace x : F(x,t)<\phi(t) \rbrace $ continuous?

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#real-analysis #continuity #supremum-and-infimum
271
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Prove that the supremum of a set of nested square roots is 2

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64
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Proving that $\sup\limits_{n\geq 1}\{a_n+b_n\}\neq \sup\limits_{n\geq 1}a_n+\sup\limits_{n\geq 1}b_n$

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#real-analysis #algebra-precalculus #proof-verification #supremum-and-infimum

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