Re: Bringing back an old tetration curiosity?

On Sep 17, 9:45 pm, mike3 <mike4...@xxxxxxxxx> wrote:
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.

The branching doesn't look to me as a side effect of possible rounding
errors. I can send you the C source code of the program, but I would
like an independent verification of the result. If your program
produces the same result (the same branching) then this will reaffirm
the result. It is not difficult to write such a program.

Theron

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