In my opinion 1/0 is undefined. Of course it's not a real number, and...
Reason 1: lim x→0+ [1/x] = +|1/0| = infinity, but lim x→0- [1/x] = -|1/0| = -infinity
(Cannot be concluded that the convergence function is positive or negative.)
Reason 2: assume 1/0 = +infinity So infinity = 1/0 = 1(-1)/[(0)(-1)] = -1/0 = -infinity
(Contradict.)
The absolute value of (1/0) is both negative as well as positive infinity as a convergence as 1+/- x approaches 0.
0 is both negative and positive. Therefore 1/0 is as well.
But the absolute value of that is indeed +infinity