Let [itex]f: \mathbb{R} \rightarrow \mathbb{R}[/itex] be given. Let [itex]L[/itex] be a real number. State the condition for saying that as [itex]x[/itex] tends to [itex]a[/itex], the limit of [itex]f(x)[/itex] is not [itex]L[/itex]. The statement ought to begin with "Given there exists [itex]\epsilon > 0[/itex]".(adsbygoogle = window.adsbygoogle || []).push({});

Best guess: [itex]\lim_{x \rightarrow a}f(x) \neq L[/itex] means, given there exists [itex]\epsilon > 0[/itex] there exists [itex]\delta > 0[/itex] such that [itex]|x-a|<\delta \Rightarrow |f(x) - L| > \epsilon[/itex]. I'm really not sure about this, however.

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# Strange limit question

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