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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 11, 2013 3:26 PM
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Dan Christensen wrote:

>
> 0^0 = 0^0 * 0^0
>
> Therefore, 0^0 = 0 or 1.

> To my knowledge, there is no purely number-theoretic justification
> for eliminating either possibility.

I'm sure this
https://en.wikipedia.org/wiki/0%5E0#Zero_to_the_power_of_zero has been
pointed out to you (either the page or the facts on the page), so your
claim seems to be wrong.

If the fact 0^0 = 0^0 * 0^0 doesn't settle 0^0 being 0 or 1, then more
data is needed. You can't just stop at
0^0 = 0^0 * 0^0 -> (0^0 = 0 or 1)
and say 0^0 is or should be undefined.

> Given this ambiguity, the prudent course is to leave 0^0 undefined
> (like division by zero), especially in general purpose programming
> languages. Currently, most programming languages seem to have 0^0 =
> 1.

In your arguments you seem to switch between mathematics and
programming. In mathematics 0^0 = 1, in programming 0^0 should be what
the specification says it should be.

--
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

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