Is one divided by zero is infinity only in programming or outside of programming too?

Question

If so then whose idea to program the console to output that, and why?
I heard other people say it undefined (maybe not in term of programming)
This is what it say in term of programming:
1/0 = Infinity....... -1/-0 = Infinity
-1/0 = -Infinity... 1/-0 = -Infinity
0/0 & -0/0 & 0/-0 = NaN

Answer 1

It's undefined, but lim(x->0) 1/x = oo

Answer 2

/0 IS just impossible .

Answer 3

in real word Mathematics, it is Undefined.