The Concept of Continuity

Continuity, in mathematics, refers to the idea that a function behaves smoothly without unexpected jumps or breaks. If a function is continuous at a point, small changes in the input near that point produce small changes in the output, ensuring no sudden jumps. Imagine drawing the graph of the function without lifting your pen; that's a visual way to understand continuity. It signifies a consistent, predictable relationship between variables, allowing us to analyze and understand the behavior of functions effectively. Continuity is fundamental in calculus and many real-world applications involving smooth, ongoing processes.