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Convergence of sequence of sups and sequence of infs of bounded sequence

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#real-analysis #sequences-and-series #convergence-divergence #supremum-and-infimum
108
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Let $\{x_n\}_{n \in\mathbb{N}}$ be a bounded sequence of real numbers. Let us define $y_n = \sup\{x_k : k \geq n\}$ and $z_n = \inf{x_k : k \geq n}.$

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#real-analysis #convergence-divergence #supremum-and-infimum #limsup-and-liminf
38
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Prove that, if $f:X\to[0,\infty)$ then $\sup([f(x)]^2)=[\sup(f(x))]^2$

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#functions #supremum-and-infimum
612
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Joint distribution of hitting times for brownian motion with drift

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#brownian-motion #supremum-and-infimum #density-function
50
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Let $A,B \subset \mathbb{R} $ nonempty sets and bounded such that $A \cap B = \emptyset $ then $sup A \ne supB$

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#calculus #supremum-and-infimum
110
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Find the $\limsup$ and $\liminf$ of $\{x_{n}\}$

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#real-analysis #convergence-divergence #supremum-and-infimum #limsup-and-liminf
53
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Infimum and bound of the inequality.

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#real-analysis #analysis #inequality #supremum-and-infimum
34
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Ways of calculating something of the sort $||f_n-f||_{\infty}$ faster

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#real-analysis #supremum-and-infimum
67
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Confusion regarding worst case robust optimization

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#optimization #convex-optimization #supremum-and-infimum #operations-research
56
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lower bound and infinimum of a function

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#real-analysis #analysis #functions #supremum-and-infimum
444
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Finding supremum and infimum of a set of rational numbers

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#real-analysis #calculus #supremum-and-infimum
50
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$f^*$ error using infimum in PAC learning

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#definition #machine-learning #supremum-and-infimum
73
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Show that in general $\inf \sup \ne \sup \inf$ for bilinear functions

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#inequality #supremum-and-infimum #bilinear-form
106
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How to prove that the supremum of this set is 0?

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#real-analysis #supremum-and-infimum
202
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distance function between point and compact set

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#analysis #compactness #solution-verification #normed-spaces #supremum-and-infimum

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