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The supremum of the function $f(x)=\frac{1-\cos Nx}{1-\cos x}$

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#real-analysis #trigonometry #supremum-and-infimum
83
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If $\sup \{a_n\mid n\in \mathbb{N}\}=1$ then $\frac{1}{1-a_n}\to\infty$

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#calculus #sequences-and-series #limits #supremum-and-infimum
104
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Prove that a sequence sup $a_n\ne1$

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#sequences-and-series #supremum-and-infimum
54
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How does this follow from the theorem?[normed linear space]

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#functional-analysis #vector-spaces #linear-transformations #supremum-and-infimum
50
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A property of infimum??

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#supremum-and-infimum
98
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$\sup(\sup) \leq 2 \inf(\sup)$

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#real-analysis #supremum-and-infimum
117
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Meaning of symbols like $\inf\limits_{\epsilon>0}$

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#soft-question #notation #supremum-and-infimum
3.2k
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What is the difference between maximal element and least upper bound?

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#real-numbers #supremum-and-infimum
8k
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If $A \subset B$, then $\inf B \geq \inf A $?

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#real-analysis #supremum-and-infimum
12.3k
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Why is the lagrange dual function concave?

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#lagrange-multiplier #supremum-and-infimum
60
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$\liminf_n a_n = \inf_n a_n$ if $a_n \ge a_m$ when $n\mid m$

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#real-analysis #reference-request #limsup-and-liminf #supremum-and-infimum
1.6k
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Find supremum and infimumm of a set with two variables

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#analysis #supremum-and-infimum
167
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Conditions for the existence of moments of the supremum of a random variable

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#random-variables #supremum-and-infimum #moment-generating-functions
2.1k
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minimum or infimum for countable sets?

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#supremum-and-infimum
291
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The range of the function $f:\mathbb{R}\to \mathbb{R}$ given by $f(x)=\frac{3+2 \sin x}{\sqrt{1+ \cos x}+\sqrt{1- \cos x}}$

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#calculus #functions #derivatives #supremum-and-infimum

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