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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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 Peter Percival Posts: 2,623 Registered: 10/25/10
Re: Leaving 0^0 undefined -- A number-theoretic rationale
Posted: Sep 12, 2013 3:45 AM

Dan Christensen wrote:
> On Wednesday, September 11, 2013 5:09:52 PM UTC-4, Peter Percival wrote:
>> Dan Christensen wrote:
>>
>>
>>

>>>
>>
>>> Show me a contradiction that arises from 0^0 = 0.
>>
>>
>>
>> The product of the empty set is 1, hence 0^0 = 1. That contradicts 0^0
>>
>> = 0. Therefore 0^0 doesn't = 0.
>>

>
> What has this got to do with number theory? You need something along the lines of 0^0=0 => 0=1.
>
> Dan
>

From 0^0=1 and 0^0=0 you can clearly deduce 0=1. If you reject the
conclusion then you must reject one of the premises. The one to reject
is 0^0=0.

--
Sorrow in all lands, and grievous omens.
Great anger in the dragon of the hills,
And silent now the earth's green oracles
That will not speak again of innocence.
David Sutton -- Geomancies