tetration base conversion, and sexp/slog limit equations

[bo198214]

I think that means converting between tetration bases, even for very large numbers, is never going to give an exact constant value, but "wobbles" a little bit.

Perhaps this is just the effect of using different slogs.
If we have two slogs for one base, say and , which are strictly increasing and have the same range of values , then
is defined and
is 1-periodic.
Or in other words for a 1-periodic function . Subtraction of both yields
.

If we consider now different bases and , and looking at the difference of
and , then we see
.

So even if would exist, then probably would be wobbly, i.e. not converge to 0.

On the other hand this could be a possible uniqueness criterion. Because if exists for one slog then would not exist for another slog but wobble around .