Chapter 5.1 relations

Define relations as sets of ordered pairs. This makes functions

Use letter rho ρ

ρ = { (1, 2),(2,4),(3,7),(2,2)}

A relation is a subset of the cartesian product of two setsx^2 + y^2 = 8

For the set of numbers{ -4 ... + 4} on each For all natural numbers or whatever there's an infinite number of pairs in the cartesian products

Interesting relations



 * 1) Reflexive relation
 * 2) Symmetric
 * 3) Transitive
 * 4) Antisymmetric

Relations examples

 * is not symmettric: 1 | 2 but not 2 | 1


 * is transitive: if a | b and b | c then a | c


 * is antisymmetric: suppose x | y and y | x,


 * x and y are eal numbers

Closure of a relation
Closure is another relation