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.

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- Dec 25th 2005, 01:05 PMThePerfectHackerExistence 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. - Dec 25th 2005, 01:20 PMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

Or have I misunderstood your intention? - Dec 25th 2005, 03:59 PMThePerfectHacker
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. - Dec 26th 2005, 12:46 PMmooshazzQuote:

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