― To be able to understand what discontinuity is, we first need to know what continuity is. The dictionary definition of continuity is: Something that goes on continuously without break. Continuity in math refers to graphing of functions. In simple terms, a function is said to be continuous if it goes on without break. Consider the following graphs for example: ∙ All the above function, are continuous as there are not breaks in the functions. Now consider the following functions: ∙ [...].