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Brandon Rozek 2025-02-16 22:04:56 -05:00
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@ -64,7 +64,7 @@ Let $s_1 > 0$ be arbitrary, and define $s_{n + 1} = \frac{1}{2}(s_n + \frac{a}{s
**Corollary:** If $X = (x_n) \subseteq \mathbb{R}$ has a subsequence that diverges then $X$ diverges.
**Monotone Sequence Theorem**: If $X = (x_n) \subseteq \mathbb{R}$, then it contains a <u>monotone subsequence</u>.
**Monotone Sequence Theorem**: If $X = (x_n) \subseteq \mathbb{R}$, then it contains a *monotone subsequence*.
**Bolzano-Weierstrass Theorem:** Every bounded sequence in $\mathbb{R}$ has a convergent subsequence.