Limit of a Sequence Equal to the Limit of a Function

Asked Jan 21 '20 at 03:55

Active Jan 21 '20 at 04:02

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If $f$ is a continuous function, then if $\lim_{x\to\infty} f(x)=L$ , then $\lim_{n\to\infty}f(n)=L$

How do I prove this theorem? I've made some attempts by using the greatest integer function but it does not seem very coherent. I'd appreciate any help!

asked Jan 21 '20 at 03:55

Joshwa Ordoñez

Are you familiar with the sequential definition of limit of a function? The result follows immediately by taking $x_n=n$. See here: https://en.wikipedia.org/wiki/Limit_of_a_function#Other_characterizations – bjorn93 Jan 21 '20 at 04:04

Limit of a Sequence Equal to the Limit of a Function

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