Let
Then proof existence of infinity or a limit (but not both):
Thus,
or
Logic caution:
In the problem you have to proof that exactly one of the conditions must be satisfied and exactly one.
Originally Posted by ThePerfectHacker
in case of infinity then for any given M there is X that for every x>X, f(x)>M
take M to be L+100 and L is not a limit
in case of L for every given g>0 there is X wich for every x>X, |f(x)-L|<g
take X to be the one that from him forward f(x) is blocked (don't remember the english expression) (and don't remember the proof that you have one) in this part f(x)<>infinity