Answer
∃ε > 0 such that ∀ integers N, ∃ an integer n such that n > N and either L − ε ≥ $a_n$ or $a_n$ ≥ L + ε. In other words, there is a positive number ε such that for all integers N, it is possible to find an integer n that is greater than N and has the property that an does not lie between L − ε and L + ε.
Work Step by Step
Recall the negation of a for all statement:
~($\forall x$ in D, P(x)) $\equiv \exists x$ in D such that ~P(x).
Recall the negation of an exists statement:
~($\exists x$ in D, P(x)) $\equiv \forall x$ in D such that ~P(x).
To negate a multiply quantified statement, apply the laws in stages moving left to right along the sentence.
