if in support of every number ε < 0 there is some number δ > 0 such that

 |f ( x ) - L |< ε                whenever                        - δ < x - a < 0 or (a - δ < x < a )

Note as well that along with both of these definitions there are two ways to deal along with the limitation on x and the one in parenthesis is possibly the easier to use, though the main one given more nearly matches the definition of the normal limit above.

Let's work a quick instance of one of these, even though as you'll see they work in much the similar manner as the normal limit problems do.