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Topic: Iterated exponentiation (tetration) to non-integral indices
Replies: 7   Last Post: Jul 13, 2000 6:16 PM

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Clifford J. Nelson

Posts: 285
Registered: 12/3/04
Iterated exponentiation (tetration) to non-integral indices
Posted: Jul 12, 2000 6:41 PM
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Iterated exponentiation (tetration) to non-integral indices:

Six to eight years ago on the Prodigy network I asked, if 2#3 is 2^(2^2)
= 16, then what is 2#(1/3). A mathematician named John George said he
didn't know but somebody somewhere had probably done some work on that.
A fellow named Arnold Benson found a formula that I used as the basis of
some Mathematica computer programs.

Somehow 2#(1/3) got defined as the number x such that x#3 = 2. The
definition is just a wild guess. I think the value should be derived
from the very definition of tetration (iterated exponentiation), but I
can't do it. The original question is still open I guess.

Cliff Nelson

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