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Topic: Formal proof of the ambiguity of 0^0
Replies: 8   Last Post: Nov 18, 2013 10:49 PM

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Dan Christensen

Posts: 8,219
Registered: 7/9/08
Re: Formal proof of the ambiguity of 0^0
Posted: Nov 18, 2013 10:49 PM
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On Monday, November 18, 2013 6:17:13 PM UTC-5, Peter Percival wrote:
> Dan Christensen wrote:

> > While 0^0 = 1 may make sense in some applications, it doesn't make
> > sense if you are trying to formalize the notion repeated
> > multiplication of natural numbers. As I have shown here, it is only
> > one of infinite possibilities.
> You count 0 among the natural numbers, don't you?

For the purposes of this discussion, yes.

> If you can multiply
> any finite number of numbers together, say n of them, then the case n =
> 0 ought to be included.

You mean x^0?

> So if you multiply the numbers in the empty set
> together what do you get?

Surely, you aren't going suggest that the answer is 1. Not that it would be relevant in any case.

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