Formal Definition of Epsilon-Delta Limits; Finding Delta given an Epsilon (Limits) Infinity with Epsilon-Delta; Limit Does Not Exist with Epsilon-Delta; See Also. Epsilon Delta Limit Proofs at and going to infinity. . the statement is that if you get close enough to x = 0, the function gets arbitrarily large. They are like $\epsilon-\delta$ proofs Limits at infinity often occur as limits of sequences, such as Rearranging the inequality, I get $n > \dfrac{1}{\epsilon}$.