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$\limsup_n a_n+b_n+c_n+\limsup_n b_n \le \limsup_n a_n+b_n+\limsup_n b_n+c_n$?

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#real-analysis #sequences-and-series #limsup-and-liminf
55
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Some basic questions about definitions of sup an inf

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#proof-verification #limsup-and-liminf #epsilon-delta
51
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$\limsup_n a_n + \limsup_n b_n \le \limsup_n c_n + \limsup_n d_n$ if $a_n+b_n=c_n+d_n$ and $a_n$ maximum

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#real-analysis #real-numbers #limsup-and-liminf #supremum-and-infimum
32
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Is $\exists p\in\mathbb{N}:\frac{1}{\left| n^p \sin(n/2) \right|}$ is bounded for $n \in \mathbb{N}$?

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#limits #trigonometry #limsup-and-liminf
176
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Does $\lim_{n\to \infty}\sigma_n=0\implies \lim_{n\to \infty} a_n=0$?

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#real-analysis #sequences-and-series #limits #examples-counterexamples #limsup-and-liminf
1.3k
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The proof of theorem 3.19 from baby Rudin

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#real-analysis #inequality #proof-verification #limsup-and-liminf
87
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A question on convergent series of positive terms

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#sequences-and-series #convergence-divergence #limsup-and-liminf
50
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$ 1+\mathsf{d}^\star(B) \le \mathsf{d}^\star(A\cup B)+\mathsf{d}^\star(B\cup C) $ with $A\cup B\cup C=\bf{N}^+$

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#real-analysis #number-theory #limsup-and-liminf
469
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Wheeden-Zygmund exercise

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#analysis #limsup-and-liminf #supremum-and-infimum
73
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Prove the following properties of sequence

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#real-analysis #limsup-and-liminf #supremum-and-infimum
714
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What is $\limsup_{n\to\infty} \frac{p_{n+1}}{p_n}$?

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#number-theory #prime-numbers #limsup-and-liminf
133
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Is there a way to find $\limsup$ and $\liminf$ for ergodic processes almost surely?

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#expectation #limsup-and-liminf #ergodic-theory #stationary-processes
88
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Knowing that liminf $x_n$ and limsup $x_n$ are in [-1,1], how to express this using big-O, small-o notation?

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#real-analysis #asymptotics #limsup-and-liminf
136
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Inequality with $\limsup$ and $\liminf$ of a sequence

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#sequences-and-series #recurrence-relations #limsup-and-liminf
18.3k
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Does a limit exist at a cusp or sharp point

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#calculus #limits #limsup-and-liminf

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