Question

What is jump discontinuity in math?

Answer 1

A jump discontinuity is when a function "jumps" from one value to another value at a point.

Explanation:

Define a function `f`. There exists a jump discontinuity at a point `a` if `lim_(x->a^-)f(x)=alpha` and `lim_(x->a^+)f(x)=beta` such that `alpha` and `beta` are real numbers (excluding `+-oo`) and `alpha!=beta`. An example is the signum function `sgn(x)=|x|/x` at `x=0`. Since `lim_(xrarr0^-)sgn(x)=-1` and `lim_(xrarr0^+)sgn(x)=1`, there is a jump discontinuity at `x=0`.