Infinity is not in the set of Real numbers so subtraction with these symbols is undefined.
Inf – Inf shows up in the context of calculus as an indeterminate form; sqrt(x-1) – sqrt(x+1) is a difference of two functions that each grow without bound (to infinity) as x grows without bound (to infinity), however, it can be shown that their difference as x grows to infinity is finite (0).
But other pairs of functions lead to different results. Depending on the f(x) – g(x), as x goes to infinity this can approach other finite numbers, or positive infinity, or negative infinity. Hence the name, indeterminate form.

Uh I mean who turned those 8's sideways