One method is purely algebraic and the other is geometric. So, where exactly did δ = ε / 2 δ = ε / 2 come from? There are two basic approaches to tracking down δ. ” The phrase “there exists” in a mathematical statement is always a signal for a scavenger hunt. The definition continues with “there exists a δ > 0. By stating “Let ε > 0 ,” ε > 0 ,” we signal our intent to do so. ” This means we must prove that whatever follows is true no matter what positive value of ε is chosen. The first part of the definition begins “For every ε > 0. With these clarifications, we can state the formal epsilon-delta definition of the limit. The statement 0 The statement | f ( x ) − L | It is also important to look at the following equivalences for absolute value:
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