Advertisement

Sequences

  • Peter Leslie Walker

Abstract

A sequence is simply a set whose elements are labelled by the positive integers (though a more formal definition is given in the next section). We write a sequence in the form s = (s1,s2, s3,…) where the dots indicate that the list of terms continues indefinitely, so that any term, for instance s491, is available for consideration if required. More explicitly we write s = (s1, s2, s3,…, sn,…) to indicate the nth term, or simply s = (2n) 1 . But sn alone (no parentheses!) is not the name of a sequence, it is the name of a number which is the nth term of a sequence. For instance s = (2n - 1) 1 is the sequence of odd integers, s = (1,3,5,…) whose nth term is sn = 2n - 1.

Keywords

Cauchy Sequence Convergent Subsequence Peak Point Convergent Sequence Finite Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag London 2004

Authors and Affiliations

  • Peter Leslie Walker
    • 1
  1. 1.College of Arts and ScienceAmerican University of SharjahSharjahUnited Arab Emirates

Personalised recommendations