[Edu-sig] 0 to the 0

Lloyd Hugh Allen lha2@columbia.edu
Thu, 25 Jul 2002 19:30:02 -0400

Urner wrote,

> Question:  why do both J and Python define 0**0 (or 0^0 in J)
> to be 1, when mathematicians (and Wolfram's Mathematica) call
> this undefined?  Speaking of Wolfram, I did the simplest
> cellular automata from NKS in J.  Output looks like this:
> http://www.inetarena.com/~pdx4d/ocn/graphics/Jnks1.png (this
> is after doing similar stuff in Python -- posted about it to
> this list in late May of this year).

For what it's worth, often it is convenient to define 0**0 to be 1--if I
recall correctly, Maple's 0**0 has a value based on context, where
x**0|x=0 is one and 0**x|x=0 is zero. Straight-out 0**0 was undefined.
All of this is based on a demo copy on a hard drive that no longer
exists, but I seem to remember coming across that and thinking it was