Relations: Especially on (Integer) Sequences

Part of the Undergraduate Topics in Computer Science book series (UTICS)


The two objectives of this chapter are (1) to provide an ordering of sequences of objects so they can be sorted, like individual numbers, and so any finite set of them can be generated in a natural order from the first to the last, and (2) to provide a mechanism for classifying complexity functions by their rates of growth.

Relations in general are defined, then equivalence relations, then order relations.

Relations on sequences of numbers are given, in particular Lexicographic-Order. Relations on infinite sequences of real numbers (including complexity functions of algorithms) are then covered with Big-Oh, Big-Theta, and Little-Oh notation.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsBrock UniversitySt. CatharinesCanada
  2. 2.Department of Computer ScienceUniversity of CalgaryCalgaryCanada

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