I was fiddling around with the definition of limits at infinity and believe I have found a statement that is equivalent to the definition.(adsbygoogle = window.adsbygoogle || []).push({});

So the question is this: are the following two statements equivalent?

(1) [tex]\lim_{x\rightarrow\infty}f\left(x\right)=L[/tex]

(2) [tex]\exists c>0\exists M>0\left(\sup\left\{ \left|x\left(f\left(x\right)-L\right)\right|:x\geq c\right\} \leq M\right)[/tex]

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# A statement equivalent to the definition of limits at infinity?

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