/lit/ - Literature

>>10437994
>when the split runs vertically
Basically, yes! That's called a hyperbola, and that split is its asymptote -- for 1/x, the asymptote is x=0, for example.
I'd be careful with that exact definition, though. The Riemann zeta function, which is the infinite sequence of 1/(1^x) + 1/(2^x) + 1/(3^x) + 1/(4^x) + ..., has one-sided limits even though it's TECHNICALLY actually continuous with no split (at x=1 there's a pole because it's infinity, specifically 1 + 1/2 + 1/3 + 1/4 which strangely enough does not converge; funnily enough, you'd expect x=-1 to also have a pole because it'd be 1 + 2 + 3 + 4 + ... and you would understandably expect that to be infinity, but due to mathematical fuckery, 1 + 2 + 3 + 4 + ... = -1/12).