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proof: Limit of self-super-roots is e^1/e. TPID 6
#1
In reply to
http://math.eretrandre.org/tetrationforu...73#pid4073

First it is easy to see that for :

( is the lower fixed point of )

Hence for we have for all :
(*)

We also know that for , quite fast, particularly for each there is an such that for all :
(**) .

Now we lead proof by contradiction, suppose that
where .

Then there must be a subsequence and such that this subsequence stays always more than apart from :
.
I.e. there is and such that
either or .

By (*) and (**) we have such that for all :
and .
As is monotone increasing for we have also
and .

This particularly means and hence none of the can be the self superroot, in contradiction to our assumption.
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Messages In This Thread
proof: Limit of self-super-roots is e^1/e. TPID 6 - by bo198214 - 10/07/2009, 08:00 AM

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