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


Adding elements of the cartesian product allows the achivement of all of these properties except antisymmettry. This means that the full cartesian product as 123 but not 4
 * 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 real numbers

Closure of a relation
Closure is another relation