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Supremum of Continuous Functions (Least Upper Bound)

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#real-analysis #continuity #supremum-and-infimum #upper-lower-bounds
176
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Least Upper Bound of Rational Numbers

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#real-numbers #supremum-and-infimum #rational-numbers
374
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How do I prove that $\sup|A|=\max(-\inf A,\,\sup A)$?

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#real-analysis #supremum-and-infimum
2.4k
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A closed bounded set contains its supremum

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#real-analysis #proof-verification #supremum-and-infimum
758
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If $f$ is bdd, integrable, $F(x) = \int_a ^x f$ for $x \in [a,b]$, prove $F$ unif continuous, differentiable & continuous at any $c$, $F'(c) = f(c)$

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#calculus #real-analysis #differential-topology #supremum-and-infimum #riemann-integration
145
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If $f_n$ is continuous for all $n\in \mathbb{N}$ is $f(x)=\sup(f_n(x))$ continuous?

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#calculus #real-analysis #sequences-and-series #supremum-and-infimum
167
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Proof of non-emptiness of a set

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#real-analysis #infinity #supremum-and-infimum #convention
1k
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Equivalence of sup-Norm in metric space induced by norm

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#general-topology #functional-analysis #metric-spaces #normed-spaces #supremum-and-infimum
1.3k
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Let $\{x_n\}$ be a bounded sequence and $s=\sup\{x_n|n\in\mathbb N\}.$ Show that if $s\notin \{x_n|n\in\mathbb N\}, $then there exists a subsequence .

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#real-analysis #sequences-and-series #supremum-and-infimum
133
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Largest Fraction Smaller than a Given Fraction

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#prime-numbers #supremum-and-infimum #integers
147
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Understanding Content in Baby Rudin

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#real-analysis #real-numbers #irrational-numbers #supremum-and-infimum #rational-numbers
84
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Probability of supreme of chi-squared distribution

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#probability #normal-distribution #supremum-and-infimum #chi-squared
4k
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Inequality involving supremum and integral

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#real-analysis #integration #functions #supremum-and-infimum
323
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sup as a colimit

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#category-theory #supremum-and-infimum
50
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Supremum (pairwise disjoint functions)

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#supremum-and-infimum

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