Epsilon and Delta Theories

Epsilon-Delta theories in calculus define how functions behave near a specific point. They formalize the idea of a function getting arbitrarily close to a value: for any small margin of error (epsilon), there exists a distance (delta) around the point such that if you stay within that distance, the function's output stays within the epsilon margin. This precise language ensures we understand limits rigorously, confirming how functions approach a particular value as inputs approach a specific point, helping to establish the foundations of calculus with clarity and consistency.