What is the difference between a jump and a removable discontinuity?

1 Answer
Nov 14, 2015

Their limit definitions and appearance on a graph.


This is a jump discontinuity. Wikimedia
In a jump discontinuity, #lim_(x->a^-)f(x)!=lim_(x->a^+)f(x)#. That means, the function on both sides of a value approaches different values, that is, the function appears to "jump" from one place to another.

This is a removable discontinuity (sometimes called a hole).
Here, the function appears to come to a point, but the actual function value is elsewhere or does not exist.This can be written as #lim_(x->a^-)f(x)=lim_(x->a^+)f(x)!=f(a)#