the principle of continuity

The principle of continuity states that in a smooth, unbroken flow, small changes in the input result in small changes in the output. If a function is continuous at a point, it means there's no sudden jump or gap there; the function's values approach a single, well-defined number from both sides. This concept applies to many real-world scenarios, such as water flowing smoothly through a pipe without disruptions. Essentially, continuity ensures a seamless transition in a system, making it predictable and stable as conditions change gradually.