Descriptive definition of sequence limit: For sequence {yn}, there is a constant a. If yn approaches a infinitely when n increases infinitely (| yn-a | infinitely approaches 0), it is said that {yn} takes a as the limit when n approaches infinity. Yn→A(n→∞). A finite sequence is called convergent sequence, otherwise it is called sequence divergence. If the sequence {yn} takes a as the limit, it is also called that {yn} converges to a.

Accurate definition of sequence: there are sequence {yn} and real number A. If there is any given positive integer ε, no matter how small, there is always a positive integer N, when n >; n，πyn-πa