Thread: 0^0 = 1?
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Apr14-05, 02:45 PM
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Quote Quote by CRGreathouse
I don't think that it's undefined; I think that it's 1. 0^0 is an empty product, and empty products are necessarily equal to 1. As Galileo points out above, we need 0^0=1 for series to have compact formulas.

Everyone agrees that [tex]x^0=1[/tex] for [tex]x\neq0[/tex], but there's no reason to think that it should be different at 0 -- [tex]0^x[/tex] is only 0 for x > 0, since it's not defined for negative x.

There's no problem accepting 0^0 as 1, and there are many good reasons to think it shouldn't be undefined or 0.
That's not mathematical at all. I've always had a simple way of looking at it:

[tex]x^0 = \frac{x}{x}[/tex].