Mathematical continuity

Mathematical continuity describes a property of functions where small changes in the input produce small changes in the output, with no sudden jumps or gaps. Imagine drawing a curve without lifting your pen; if you can do so smoothly from start to finish, the function is continuous at every point. Formally, a function is continuous at a point if its value matches the limit when approaching that point from both directions. Overall, continuity ensures a function behaves predictably and smoothly, without unexpected breaks or holes, enabling meaningful analysis and interpretation.