On Wednesday, September 11, 2013 3:26:05 PM UTC-4, Peter Percival wrote: > Dan Christensen wrote: > > > > > > > > 0^0 = 0^0 * 0^0 > > > > > > Therefore, 0^0 = 0 or 1. > > > > > > > To my knowledge, there is no purely number-theoretic justification > > > for eliminating either possibility. > > > > I'm sure this > > https://en.wikipedia.org/wiki/0%5E0#Zero_to_the_power_of_zero has been > > pointed out to you (either the page or the facts on the page), so your > > claim seems to be wrong. >
I see there no purely number-theoretic justification (no limits or real numbers) that would eliminate 0^0 = 0 as a possibility. Note: Citing applications (like BT) where 0^0 = 1 is convenient an 0^0 = 0 is inconvenient is not enough.
> > > If the fact 0^0 = 0^0 * 0^0 doesn't settle 0^0 being 0 or 1, then more > > data is needed. You can't just stop at > > 0^0 = 0^0 * 0^0 -> (0^0 = 0 or 1) > > and say 0^0 is or should be undefined. >
Show me a contradiction that arises from 0^0 = 0.
Example: A contradiction arises from 0^0 = 2 by substituting into 0^0 = 0^0 * 0^0. 2=/=4.
> > > > Given this ambiguity, the prudent course is to leave 0^0 undefined > > > (like division by zero), especially in general purpose programming > > > languages. Currently, most programming languages seem to have 0^0 = > > > 1. > > > > In your arguments you seem to switch between mathematics and > > programming.
In the purely formal world of programming, the issue is somehow brought into sharper focus. In programming, there is no special "context" for arithmetic operators.
> In mathematics 0^0 = 1, in programming 0^0 should be what > > the specification says it should be. >