Let [tex] X [/tex] be a metric space, let [tex] a \in X [/tex] be a limit point of [tex] X [/tex], and let [tex] f: X \to \mathbb{R} [/tex] be a function. Assume that the limit of [tex] f [/tex] exists at [tex] a [/tex]. Fix [tex] t \in \mathbb{R} [/tex]. Suppose there exists [tex] r > 0 [/tex] such that [tex] f(x) \geq t [/tex] for every [tex] x \in B_{r}(a) \backslash \{a \} [/tex]; then [tex] \lim_{x \to a} f(x) \geq t [/tex].(adsbygoogle = window.adsbygoogle || []).push({});

How would you prove this? Would you use Trichotomy?

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# Homework Help: Would you use Trichotomy?

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