CAS: 0/0 is undefined, however 1/0 is infinite?

[Albert Chan]

(10-23-2018 11:07 AM)sasa Wrote:  Definition: Any number powered by 0 is 1.

Let prove first that 0^0 is 1 :
x^0 = 1
0 * ln(x) = ln(1)
0 * ln(x) = 0
But we have a problem now...

ln(0) = -infinity
0 * (-infinity) = 0
(-infinity) = 0/0
(-infinity)= undef

I do not follow why you are allowed to divide 0 from both side, getting:

ln(x) = 0/0 = undef ?

Following this logic, not only 0^0 ≠ 1, for any x, x^0 ≠ 1 ...