Continuity refers to the idea of something remaining consistent or unbroken over time. In storytelling, for example, continuity ensures that characters, events, and settings remain logical and coherent throughout a narrative. This helps the audience follow the plot without confusion, making the experience more enjoyable. In mathematics, continuity describes a property of functions where small changes in input lead to small changes in output. For instance, the function of a straight line is continuous because you can draw it without lifting your pencil. This concept is crucial in calculus, where it helps in understanding limits and derivatives, such as those involving functions and graphs.