Date: Oct 17, 2013 5:40 PM
Author: Dan Christensen
Subject: Re: Formal proof of the ambiguity of 0^0
On Thursday, October 17, 2013 4:15:41 PM UTC-4, Bart Goddard wrote:

> Dan Christensen <Dan_Christensen@sympatico.ca> wrote in

>

> news:daf56be5-9c90-4648-b998-9d8649d01eb4@googlegroups.com:

>

>

>

> >> 3^2 = (0^0)^2 = 0^(2*0) = 0^0 = 3

>

> >>

>

> >

>

> > Good point! That's why I stipulate that a non-zero base for the Power

>

> > of a Power Rule (Theorem 5) which you use in your 2nd step.

>

>

>

> Which is why you have nothing but contradictions here. You're

>

> asserting that 0^0 can be defined to be anything, and the

>

> exponent rules still work.

You can avoid the contradictions by stipulating non-zero bases in each of the Laws of Exponents, as I have done here (see Theorems 4,5 and 7). It's no big deal. While there are still some hold-outs for 0^0=1, mathematicians have been leaving 0^0 undefined in this way for nearly two centuries (starting with Cauchy in the early 19th century).

Dan

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