04/25/2010, 03:19 PM
(10/23/2009, 01:18 AM)andydude Wrote: If you liked that, you might enjoy this graph too. This is x^^(-1/2), same color scheme.
It appears that the limit \( \lim_{x\to 1} {}^{(-1/2)}x = 1 \) which I was surprised to see. It really is true that a picture is worth 1000 words.
this is an old post , but has this been explained already ?
maybe its just that x^^y = 1 for all x = 1.
or is that too simple ?
i really feel that - after being some time on the forum - the most intresting stuff , closed form but unproven , are almost always limits.
limits are gaining territory in tetration.
one could almost split up the forum into
matrix
contour integral
sums and products
limits
are all solutions to tetration consistant with x^^y = 1 for all x = 1 ?
andrew's method is not ?
( my own method is designed for bases > eta )
regards
tommy1729