Let (left{x_{n}ight}_{n=1}^{infty}) be a sequence of real numbers. a. Prove that [inf _{n in mathbb{N}} x_{n} leq

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Let $\left\{x_{n}ight\}_{n=1}^{\infty}$ be a sequence of real numbers.

a. Prove that

\[\inf _{n \in \mathbb{N}} x_{n} \leq \liminf _{n ightarrow \infty} x_{n} \leq \limsup _{n ightarrow \infty} x_{n} \leq \sup _{n \in \mathbb{N}} x_{n}\]

b. Prove that

\[\liminf _{n ightarrow \infty} x_{n}=\limsup _{n ightarrow \infty} x_{n}=l\]

if and only if

\[\lim _{n ightarrow \infty} x_{n}=l\]

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Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

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Question Posted: Mar 15, 2024 02:01 AM

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Let (left{x_{n}ight}_{n=1}^{infty}) be a sequence of real numbers. a. Prove that [inf _{n in mathbb{N}} x_{n} leq

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Introduction To Statistical Limit Theory

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