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.
http://math.eretrandre.org/tetrationforu...73#pid4073
First it is easy to see that for
Hence for
(*)
We also know that for
(**)
Now we lead proof by contradiction, suppose that
Then there must be a subsequence
I.e. there is
either
By (*) and (**) we have
As
This particularly means