Date: Oct 30, 2013 5:15 PM
Author: Bart Goddard
Subject: Re: Formal proof of the ambiguity of 0^0

Dan Christensen <Dan_Christensen@sympatico.ca> wrote in
news:8c1d6b6d-986e-4fd5-b7ec-3b1236964c2c@googlegroups.com:


>> You're claiming to extend exponentiation to N_0, but
>>
>> all of your rules say "nonzero base."

>
> [snip]
>
> Nothing wrong with that.


In mathematics, contradiction is the ONLY sort of wrong
there is. And you're definitely contradicting yourself.
You're extending without extending.


> Mathematicians have being doing this
> implicitly for nearly two centuries. Now, it has a rigorous
> foundation.


No, they have not. I'm trying to imagine a mathematician
"extending" real number multiplication
to the complex numbers, but declaring, in all parts
of his definition, that it doesn't apply to non-real
numbers. And, as if that wasn't bizarrely stupid
enough, to follow up with "therefore it doesn't matter
how you define complex multiplication...."


> 0^0 is an unspecified natural number.

If it's not specified, then it's not defined.
If it's not defined, there is no extention.


> Again, my definition refers specifically to 0-exponents, and I have
> referred here to a theorem concerning 0-bases that can be derived from
> that definition. Sure sounds like "extending" to me.


But you've shown yourself to be a particularly bad
judge of what an extention is, so that fact that it
sounds like it "to you" means nothing. (And, in fact,
actually argues against.) You can't claim an extention
to N_0, unless 0^0 is defined.