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