I read that "if f : R -> R is an increasing function, then limit as x tend to infinity of f(x) is either infinity, minus infinity or a real number". f an increasing function means { x < y } => { f(x) < or = f(y) }.(adsbygoogle = window.adsbygoogle || []).push({});

How do I prove this (if it is true)? Can I apply this to a function g : R -> [0,1]?

P.S.

I am not looking for a precise proof. A loose discussion of the way to prove this would be fine.

Thanks!

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# Limits of Functions at Infinity

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