CHAPTER 5: EQUIVALENCE RELATIONS AND EQUIVALENCE ...

184 downloads 188337 Views 157KB Size Report
Proof: To see that ≃ is reflexive, let x ∈ R. Then x − x = 0 and 0 ∈ Z, so x ≃ x. .... Comment: Later we will begin to treat an equivalence class as a single ..... bd . Solution: (a) “∗” is not defined if y = 0. (b) The set of nonzero integers is not closed ...
CHAPTER 5: EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES

Section 5.1: Equivalence Relations Relations Examples of relations on the set of real numbers include “=”, “