Tilted Forum Project Discussion Community - View Single Post - Why does a number raised to the zero = 1?

Yakk · 06-07-2004, 05:50 AM

RSL, how was it decided that
x^(1/100) = 100th root of x

They took the arithmetically true statements (x^a*x^b = x^(a+b), (x^a)^b = x^a*b, etc, where x^a = x*x*..*x (a times)), and extended them to the rationals, then the reals.

x^(1/2) = square root of x
because
x^(1/2) * x^(1/2) = x^(1/2+1/2) = x
the non-rational reals are then defined by making the function continuous (which also, independantly, results in x^0 = 1 for all x not equal to zero).

Interestingly, f(x,a) := x^a is not continuous everywhere: f(0,a) either has a discontinuity at a=0, or f(x,0) has a discontinuity at x=0. Hence the 0^0 problem.

06-07-2004, 05:50 AM	#8 (permalink)
Yakk Wehret Den Anfängen! Location: Ontario, Canada	RSL, how was it decided that x^(1/100) = 100th root of x They took the arithmetically true statements (x^ax^b = x^(a+b), (x^a)^b = x^ab, etc, where x^a = xx..x (a times)), and extended them to the rationals, then the reals. x^(1/2) = square root of x because x^(1/2) x^(1/2) = x^(1/2+1/2) = x the non-rational reals are then defined by making the function continuous (which also, independantly, results in x^0 = 1 for all x not equal to zero). Interestingly, f(x,a) := x^a is not continuous everywhere: f(0,a) either has a discontinuity at a=0, or f(x,0) has a discontinuity at x=0. Hence the 0^0 problem. __________________ Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.