ε-δ Definition

The ε-δ (epsilon-delta) definition is a formal way to specify what it means for a function to approach a particular value as inputs get closer to a certain point. It states that for any small number ε (representing how close we want the output to be to the target value), there exists another small number δ such that whenever the input is within δ of the point, the output will be within ε of the target. Essentially, it rigorously describes how closely a function's outputs can be controlled by careful choices of input proximity.