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Topic: Leaving 0^0 undefined -- A number-theoretic rationale
Replies: 48   Last Post: Sep 15, 2013 1:06 PM

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 Dan Christensen Posts: 8,219 Registered: 7/9/08
Re: Leaving 0^0 undefined -- A number-theoretic rationale
Posted: Sep 12, 2013 12:26 AM

On Wednesday, September 11, 2013 5:09:52 PM UTC-4, Peter Percival wrote:
> Dan Christensen wrote:
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> >
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> > Show me a contradiction that arises from 0^0 = 0.
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> The product of the empty set is 1, hence 0^0 = 1. That contradicts 0^0
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> = 0. Therefore 0^0 doesn't = 0.
>

You are talking about some other set-theoretic notion of exponentiation, not the usual arithmetic operator that we are discussing here.

More convincing would be obtaining a contradiction by assuming only 0^0=0 along with the usual rules of natural-number arithmetic, including the usual Laws of Exponents.

Dan