2. Zero as a real number in a series, such as the example of temperature. Consider a formula like the combined gas law: [pressure]x[volume]/[temp]=[constant]. Is a temperature of 0 degrees Celsius indeterminate? Of course not. However, if you switch it to Kelvin, in which zero can be described as the absence of heat, then you're back to the previous definition.

According to this use of zero, 0^0 = 1 would be a much more logical and useful answer.

actually, no. In the Kelvin scale, 0 is the impossible temperature in that its absolute zero and cannot be reached according to physical laws (not for our lack of trying). This has a certain beauty to it because Kelvin is used for all the important equations, and dividing by Kelvin in this case can

*never* be indeterminate because the temperature on the Kelvin scale could never be 0

THE RULE IS THAT ANYTHING TO THE POWER OF ZERO IS ONE.

*x*^{2} =*x*^{2-2}=*x*^{0} =1

*x*^{2}

that's the basic rule, yes, but it has one exception. I don't know how old you are or if you've taken Function Algebra yet but two functions can be

**equal** but not

**equivalent**. For example, take these two functions:

f(x) = x

^{2} / x

g(x) = x

f(x) equals g(x), right? That's true, but the functions are not

*equivalent* because the DOMAIN of f(x) is different than that of g(x). Domain(f(x)) = all real numbers EXCEPT ZERO, while any real number can be plugged into g(x)

that's the same case with your rule. The domain rejects 0 if you try to plug it into x. What is 0

^{2}/0

^{2}?? It's commonly agreed that 0/0 cannot be determined by itself. Your own rule says that 0

^{2}/0

^{2} reduces to 0

^{0}.... same with 0

^{1}/0

^{1}, 0

^{5}/0

^{5}. I'm not sure if multiple zero-by-zero divisions stack up in different ways (cuz it seems to lose communitivity) but essentially you're saying that x/x = x^0 = 1. Well think of those three things as f(x), g(x), h(x). Are they equal? Yes! Are they equivalent? No! The domain is different in x/x, but laws lead that to x^0 without reduction of domain if I'm not mistaken. But dividing out the x's in the secodn one to reach 1

*does* change the domain

edit ~ I've been looking around and a lot of mathematical rules depend on 0^0 = 1 for the special cases of their functions, like factorial and combinatorics and things. So can a thing be indeterminate (ie, i've always thought that 0^0 = CANNOT BE DETERMINED) but assumed to be a set value for the use of a function?

**Edited by unreality, 07 March 2009 - 03:54 PM.**