Continuity preservation under limits refers to the property of continuous functions where the limit of a function at a point is equal to the value of the function at that point. This means that if you have a sequence of inputs approaching a specific value, the outputs will also approach the corresponding output value of the continuous function, ensuring there are no jumps or breaks in the graph. This property is crucial in understanding how uniformly continuous functions behave as they are evaluated at points close to each other.
congrats on reading the definition of continuity preservation under limits. now let's actually learn it.