Re:What does 0^0 equal? Why do mathematicians and high schoo...
by mturmon on Thursday August 25, 2011 @02:56PM
(#2925999)
I agree with you and lotharbot that if you view things from a continuous perspective, 0^0 is indeterminate.
Thinking back on my math education, part of the difference in viewpoint may be the first time I rigorously met the continuous-domain exponential.
This was in real analysis. Exponentiation is defined first for positive integer exponents, and then for rational exponents. All elementary. Then it's extended to real-valued exponents by taking the limits of rational numbers, and appealing to continuity.
I just looked, this is exercise 6 in chapter 1 of baby Rudin.
So, because the notion of limit and continuity is embedded in this definition of the exponential function, it's natural to "approach" (groan) 0^0 as a special case, because the conditions of this definition (continuity) don't hold.
Thinking back on my math education, part of the difference in viewpoint may be the first time I rigorously met the continuous-domain exponential.
This was in real analysis. Exponentiation is defined first for positive integer exponents, and then for rational exponents. All elementary. Then it's extended to real-valued exponents by taking the limits of rational numbers, and appealing to continuity.
I just looked, this is exercise 6 in chapter 1 of baby Rudin.
So, because the notion of limit and continuity is embedded in this definition of the exponential function, it's natural to "approach" (groan) 0^0 as a special case, because the conditions of this definition (continuity) don't hold.