0^0, what is it? Another maths topic!

[tarheel91]

zexen_lowe said:

tarheel91 said:

zexen_lowe said:

Galaki said:
0^0 = 1
Because anything to the power 0 equals 1.
In this case, you don't use 0 for division but just give it a representative symbol.

Anything divides by itself equals 1.

At least, that's vaguely what I remember from school.

And 0 to any power is 0.

The correct answer for 0^0 is indeterminate. There are some mathematical branches who use 0^0=1 to avoid complications and needing to create specific rules for it, but in general is treated as 0^0=Indeterminate

 

 

No, it's only indeterminate as you're approaching it.  At 0^0, it's precisely 1.  People confuse it because it's considered indeterminate as a limit and you can use L'Hospital's rule with it.  It's just like 1^Infinity.  1^Infinity is 1, but the limit as something approaches it is indeterminate.

I may be mistaken, but I think it's actually the otrer way. The limit of 0^0 does exist (and can be calculated by L'Hôpital's rule) and equals to 1, but 0^0 is indeterminate. I checked with my calculator, (1*10^-9)^(1*10^-9)= 0.999999999..., but 0^0=Ma Error

Wikipedia says this:

The evaluation of 0⁰ presents a problem, because different mathematical reasoning leads to different results. The best choice for its value — and indeed, whether or not to consider 0⁰ indeterminate (i.e., undefined) — depends on the context. According to Benson (1999), "The choice whether to define 0⁰ is based on convenience, not on correctness."^[2] There are two principal treatments in practice, one from discrete mathematics and the other from analysis.

 

In many settings, especially in foundations and combinatorics, 0⁰ is defined to be 1. This definition arises in foundational treatments of the natural numbers as finite cardinals, and is useful for shortening combinatorial identities and removing special cases from theorems, as illustrated below. In many other settings, 0⁰ is left undefined. In calculus, 0⁰ is an indeterminate form, which must be analyzed rather than evaluated. In general, mathematical analysis treats 0⁰ as undefined^[3] in order that the exponential function be continuous.

 

Anyway, we can agree that it's difficult to prove a result, if even mathemathicians can't decide a unique one, we won't decide it in a forum debate

That's interesting, I always thought the debate depended on which way you used it because it obviously has different meaning and values when it's a limit and when it's a number and so on.

What the limit actually is depends on how you're approaching 0^0, obviously.