Re: Bringing back an old tetration curiosity?

On Sep 17, 11:22 am, theronr...@xxxxxxxxx wrote:
On Sep 17, 6:12 pm, theronr...@xxxxxxxxx wrote:
<snip>
After rethinking I think that the above statement is a bit
speculative. However I'm sure that there is no continuous f: (-2; +oo)
-> R that satisfies (1), (2) and (3). Here is why:

http://img403.imageshack.us/img403/1466/sqrttetrxjx1.png

This is a 5000x5000 plot of f(x) for -1 <= x <= 0 <= y <= 1.

Theron

This is interesting. There appears to be a gentle undulation
in it, oddly enough. It's intriguing to examine that in light
of a graph of ^x (0.1) on the integers, which oscillates quite
a bit.

I'd be curious to see your program, to root out various sources
of approximation error, for example, though.

However if the method is indeed flawed, then it just might be
possible that tetrating something to the one half does indeed
take the square tetraroot after all...

.