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Mathematics LibreTexts

7.7: Summary

( \newcommand{\kernel}{\mathrm{null}\,}\)

  • Important definitions:
    • relation, binary relation
    • reflexive, symmetric, transitive
    • equivalence relation
    • equivalence class
    • modular arithmetic
    • integers modulo n
    • well-defined
    • partition
  • Modular arithmetic is an important example of the use of equivalence classes.
  • Functions must be well-defined.
  • Every binary relation can be drawn as a digraph.
  • Every partition gives rise to an equivalence relation, and vice versa.
  • Notation:
    • ),\(, or are used for equivalence relations
    • [a], or ˉa
    • Zn

This page titled 7.7: Summary is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Dave Witte Morris & Joy Morris.

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