section_path: Important concepts/Sequences and limits
section_name: Sequences and limits
paragraph_text: Sequences and limits
  
  A sequence is an ordered list. Like a set, it contains members (also called elements, or terms). Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Most precisely, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.
  
  One of the most important properties of a sequence is convergence. Informally, a sequence converges if it has a limit. Continuing informally, a (singly-infinite) sequence has a limit if it approaches some point x, called the limit, as n becomes very large. That is, for an abstract sequence (a) (with n running from 1 to infinity understood) the distance between a and x approaches 0 as n → ∞, denoted