Let f(x) be a real-valued function and let a be a number in the domain of f(x). If lim_(x->a^-) f(x) = L_1 !=L_2 = lim_(x->a^+) f(x), where L_1 and L_2 are real numbers, then f(x) has a jump discontinuity at a.

function | limit of a function from the left | limit of a function from the right

discontinuous function | infinite discontinuity | removable discontinuity

Bernard Placidus Johann Nepomuk Bolzano