7.7: Summary
- Page ID
- 62315
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- 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:
- \(\sim), \(\cong\), or \(\equiv\) are used for equivalence relations
- \([a]\), or \(\bar{a}\)
- \(\mathbb{Z}_{n}\)