Discrete Math › Section C · Graph theory › Topic C.8
Equivalence relations and partitions
Mathematics often treats different things as "the same" for some purpose: numbers with the same remainder, people born in the same month, triangles of the same shape. Equivalence relations make that idea exact, and they always sort a set into neat, non-overlapping groups.
In this topic
- Sameness in some respect
- The definition
- Congruence modulo n
- Worked example: congruence is an equivalence relation
- Equivalence classes
- Two classes never partly overlap
- Partitions
- Worked example: from a partition to its pairs
- Quotient sets and arithmetic on classes
- Common mistakes to avoid
- Key takeaways
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