Thread: Existence of Limit

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

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.

Let , then what is (if anything):



Or have I misunderstood your intention?

Yes, I made a mistake with what I said you are correct.
Show that if the limit is L then it cannot be infinite.
Show that if the limit is infinite then it cannot be L.

Originally Posted by ThePerfectHacker

Yes, I made a mistake with what I said you are correct.
Show that if the limit is L then it cannot be infinite.
Show that if the limit is infinite then it cannot be L.

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