Question

What does discontinuity mean?

Answer 1

In terms of real life, discontinuity is equivalent to move up the pencil wen you plot a graph function. See below

Explanation:

With this idea in mind, there is several types of discontinuity.

Avoidable discontinuity
Infinite jump discontinuity and
finite jump discontinuity

You can see this types in several internet pages. for example, this a finite jump discontinuity.

Mathematicaly, contnuity is equivalent to say that:

`lim_(xtox_0)f(x)` exists and is equal to `f(x_0)`