Equivalence Relations (notes for Students)

@inproceedings{Silberman2017EquivalenceR,
  title={Equivalence Relations (notes for Students)},
  author={Lior Silberman},
  year={2017}
}
1.2.1. Informal discussion. We fix a set X (the “universe”). Informally, a relation on X is a property of pairs of elements from X . For examples, “equality” is a property of pairs of real numbers (some pairs consist to two equal numbers, some don’t). Similarly, “less than” is a property of pairs of real numbers (we usually call that the “order relation on R”). On the other hand, f (x,y) = x+ y is not a relation – it is a function of the two variables x,y. “Is even” is not a relation on Z… CONTINUE READING