# What is discontinuity in calculus?

##### 1 Answer

I would say that a function is discontinuous at

#### Explanation:

Function

This requires that:

**1**

**2**

**3** The numbers in **1** and **2** must be equal.

In the most general sense: If

Some will then say that

Others will use "discontinuous" to mean something different from "not continuous"

**One** possible additional requirement is that

In this usage, we would not say that

A **second** possible additional requirement is that

In this usage:

For example:

But

#g(x) = { (0,"if", x,"is rational"),(1, "if", x, "is irrational") :}#

which is not continuous for any

A **third** possible requirement is that

In this usage

**My best advice** is to ask the person who will be evaluating your work which usage they prefer. And otherwise, don't worry too much about it. Be aware that there are various ways of using the word and they are not all in agreement.