What does 0^0 equal? Why do mathematicians and high school teachers disagree?

Re:What does 0^0 equal? Why do mathematicians and high schoo... by xyzzyz on Thursday August 25, 2011 @12:34AM (#2923775)

Exponential function is not defined by the axioms of real numbers, as opposed to addition and multiplication, so this point is irrelevant -- you can define it in any way you want. There's no inconvenience in defining 0^0 = 1, apart from misunderstanding the concept of limits by some people. Defining 0^0 = 1 is universal convention -- people either do it like this, or do not define 0^0 at all, which I'm fighting against.

The whole point of distinguishing some forms as "indeterminate" is to work around the fact that you're trying to conduct operations on the real numbers that are not defined

I am not. Are you? Let me reiterate: the whole concept of "indeterminate forms" (which, I repeat, is not formal at all) stems from misunderstanding the process of taking limits.

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Re:What does 0^0 equal? Why do mathematicians and high schoo... by lotharbot on Thursday August 25, 2011 @12:49AM (#2923799)

> "people either do it like this, or do not define 0^0 at all, which I'm fighting against."

I think it's silly to fight against it. There are circumstances in which leaving it undefined is good, and in which trying to define it as 1 would lead to either misunderstandings (in the case of beginners doing limits, a case you are too quick to dismiss) or actually incorrect (an equivalent problem in the hyperreals could violate the transfer principle).

It's a broad convention, but it is not universal, and it shouldn't be.

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