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F13 MA 274: HW #14 Before beginning this homework assignment, please review the guidelines for submitting homework. Remember to write down the total amount of time spent working on the assignment at the top of what you turn in. 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. ) 1