sheldonison Wrote: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 .