Continuity refers to the property of a function or a sequence that remains unbroken or consistent over a given interval. In mathematics, a function is continuous if small changes in the input lead to small changes in the output, meaning there are no abrupt jumps or gaps. This concept is important in calculus and analysis, as it ensures that limits and integrals can be effectively calculated. In broader contexts, continuity can also relate to the smoothness and consistency of processes or narratives in various fields.