A discontinuity is any point on a function where one of the three possibilities arise:
- The right-side limit is unequal to left-side limit
- The function jumps suddenly
- The function goes to infinity at a certain point in the domain.

Math Research of Victor Porton
Algebraic General Topology, Axiomatic Theory of Formulas, (generalized) limit of arbitrary function
A discontinuity is any point on a function where one of the three possibilities arise: