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Infimum of a nondecreasing right continuous step function

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Supremum over all simple closed curves of integral

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#real-analysis #multivariable-calculus #vector-analysis #supremum-and-infimum
43
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For bounded sequences, prove that if $x_n \leq y_n~\forall~n \in \mathbb{N}$ then $\text{lub}\{x_n\} \leq \text{lub}\{y_n\}$.

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#sequences-and-series #supremum-and-infimum
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Hölder-continuity of a function

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suprema and infima of sets without proof - Abbott 1.3.8

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#real-analysis #proof-verification #supremum-and-infimum
327
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Infimum and Supremum of a set

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#complex-analysis #functional-analysis #supremum-and-infimum
163
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Minimum of a Function

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#real-analysis #continuity #supremum-and-infimum
108
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Verifying if $||\cdot||$ is a norm on $V$

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#real-analysis #normed-spaces #supremum-and-infimum
39
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Evaluation of limit of the sequence

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#sequences-and-series #limits #supremum-and-infimum
251
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under what circumstances $\sup_{x \in \mathbb{R}} \{ f(x) + g(x) \} = \sup_{x \in \mathbb{R}} \{f(x) \} + \sup_{x \in \mathbb{R}} \{g(x)\}$?

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79
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How to verify the relation between the multiplication of supremum?

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2.8k
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How to deal with lim sup and lim inf?

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#real-analysis #limits #supremum-and-infimum #limsup-and-liminf
68
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minimization over all probability distributions

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#real-analysis #probability #expectation #supremum-and-infimum
261
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Rectifiable Curves: countably many and visualizing them

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#measure-theory #continuity #curves #supremum-and-infimum #visualization
70
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Two questions on $f(x)=e^{-x}+\cos x$

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#calculus #limits-without-lhopital #supremum-and-infimum

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