Date: 26 Sep 2000 08:21:40 -0700
From: Dina Zeliger
My question is not about solving a question, but more of proving the answer. I know that n^0 equals one, and there are a lot of ways to prove it. I understand those ways of proving the problem, but it doesn't seem logical nor i don't think it fits the definition of power.
A power is the product of a number multiplied by itself a given number of times. i.e. n^k = n*n*...*n (k times). This definition in right when k>0. But, if k=0, how come the product of multiplying a number by itself zero times equals one?
zero is basically nothing. its value is not a quantity, i.e. zero times something is nothing - zero. in that case, how is it possible that n^0=1. multiplying n by itself zero times equals nothing, since you don't multiply it at all.
That theory also suggests that 0^0=0, and that this expression is not indefinite. if (n^0=0) and (0^n=0) then (0^0=0).
I hope you can help me solve my problem. It is very disturbing, I have been thinking about it for a week now.