Definition of Continuity at a Point

The concept of continuity at a point is fundamental in the study of calculus and real analysis. It refers to the smoothness or uninterrupted nature of a function at a specific point in its domain. In mathematical terms, a function is said to be continuous at a point if the limit of the function exists at that point and is equal to the value of the function at that point. Understanding continuity at a point is crucial for analyzing the behavior of functions and solving various mathematical problems.