The ε-δ definition is a formal mathematical approach to defining limits, introduced by Augustin-Louis Cauchy and later refined by Karl Weierstrass. It provides a rigorous way to say that a function approaches a limit as the input approaches a particular value, using two small positive numbers: ε (epsilon) representing how close the function's value must be to the limit, and δ (delta) representing how close the input must be to the point of interest. This concept is foundational in establishing not only limits but also the continuity of functions.
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