epsilon-delta definitions

Epsilon-delta definitions provide a precise way to describe the concept of limits in calculus. They say that for any small positive number (epsilon) you choose, there exists another small number (delta) such that if a point is within delta of a certain value, then its function value will be within epsilon of the limit. Essentially, it formalizes the idea that as inputs get close to a point, outputs get close to the limit, ensuring the behavior of functions is well-defined and predictable near that point.