# What are continuous functions?

##### 1 Answer

Sep 17, 2015

#### Answer:

We may also state two alternative definitions of continuous functions, using either the sequential criterion or else using topology and open sets.

#### Explanation:

**Alternative definition number 1**

Let

Then f is continuous at x iff and only if the sequence of function values converge to the image of x undr f, ie

**Alternative definition number 2**

Let

ie,