# Definition of Continuity at a Point

## Key Questions

A simple statement can be made as follows:

#### Explanation:

The points of continuity are points where a function exists, that it has some real value at that point.
Since the question emanates from the topic of 'Limits' it can be further added that a function exist at a point 'a' if ${\lim}_{x \to a} f \left(x\right)$ exists (means it has some real value.)

The points of discontinuity are that where a function does not exist or it is undefined.

• Definition

A function $f \left(x\right)$ is said to be continuous at $a$ if ${\lim}_{x \to a} f \left(x\right) = f \left(a\right)$.

I hope that this was helpful.