F13 MA 274: HW #14
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1. E QUIVALENCE R ELATIONS
(1) Read Section 1 and 3 of the handout on equivalence relations. As you read,
take the time to work carefully through the examples.
(2) (J) Write and memorize the definition of “equivalence relation”.
(3) (J) Do Exercise 1.3
(Equivalence Relations are central in topology, geometry, abstract algebra, and “advanced”
real analysis. In topology and geometry, they are used to form new topological or geometric
objects by gluing together known objects. In abstract algebra, they are used as a way of
using properties of a subset to study properties of a superset. In analysis, they are used
to consider objects with similar properties as the somehow “the same”. In applied math,
they are useful in the study of differential equations. See if you can spot these ideas in the
examples given in the handout. )
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