Definition of Continuity at a Point
Key Questions

Answer:
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>a) f(x)# 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(x)# is said to be continuous at#a# if#lim_{x to a}f(x)=f(a)# .I hope that this was helpful.
Questions
Limits

Introduction to Limits

Determining One Sided Limits

Determining When a Limit does not Exist

Determining Limits Algebraically

Infinite Limits and Vertical Asymptotes

Limits at Infinity and Horizontal Asymptotes

Definition of Continuity at a Point

Classifying Topics of Discontinuity (removable vs. nonremovable)

Determining Limits Graphically

Formal Definition of a Limit at a Point

Continuous Functions

Intemediate Value Theorem

Limits for The Squeeze Theorem