What does 0^0 give us? Explain your answer please.

Question

valpey · Answer

We get to define it for our purposes. It is usually best to let the rule "anything to the zero power equals one" rule trump the "zero to any power is zero" rule because of some cool continuity phenomena of various sorts. I am thinking of the Gamma function or something.

goldphenoix · Answer

So your claiming that 0 to the 0th power is zero?

valpey · Answer

No, 1.

It makes things like:
$$e^x = \sum_{n=0}^{\infty}\frac{x^n}{n!}$$work even for x = 0.

goldphenoix · Answer

I'm going to 8th grade. I do not understand this. :|

valpey · Answer

0^0 = 1. But only really because that is how we prefer to define it. It makes writing a lot of cool equations simpler.

hero · Answer

0^0 violates rules of exponents because they can't figure out if it equals zero or one, so they just say it is undefined.

goldphenoix · Answer

What if 0^0 is in a problem? Do I consider it as 1 or 0?

valpey · Answer

Consider it as 1.

whpalmer4 · Answer

No, 0^0 is indeterminate.  It is sometimes defined to equal 1 for convenience.

goldphenoix · Answer

Ah, thanks. Hardest part. Who do I give the medal to? =/

whpalmer4 · Answer

I'll make that part slightly easier — don't give it to me.

goldphenoix · Answer

Thank you everyone! :)

hero · Answer

If you tell someone not to do something...

goldphenoix · Answer

What do you mean, Hero?

valpey · Answer

http://en.wikipedia.org/wiki/Exponential_function The expansion only works if e^0 = 1. Which is only true if 0^0 = 1.

whpalmer4 · Answer

http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/