Discrete Mathematical Structure, Lecture 4.2: Equivalence relations and equivalence classes

Discrete Mathematical Structure, Lecture 4.2: Equivalence relations and equivalence classes.

An equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equivalence class of an element is the set of all other elements that are equivalent to it. The set of equivalence classes partition the set. After formally introducing these examples, we spent the remainder of the lecture giving example of equivalence relations and classes, including isomorphic graphs, similar matrices, arbitrary partitions, bit strings under Hamming weight, digital logic circuits, modular arithmetic, and constructing the rational numbers from the integers. We also spend some time understanding what it means for a binary operation to be well-defined with respect to an equivalence relation.

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