# Limit of a sequence

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The mathematical concept of limit of a sequence provides a rigorous definition of the idea of a sequence converging towards a point called the limit.

Suppose x1, x2, ... is a sequence of real numbers. We say that the real number L is the limit of this sequence and we write

${\displaystyle \lim _{n\to \infty }x_{n}=L}$

if and only if for every real number ε > 0 there exists a natural number n0 such that for all n > n0 we have |xn − L| < ε. The number n0 will in general depend on ε.