0

I'm teaching my self set theory id iv gotten to the point of relations. I understand a relation between two sets is any subset formed from the Cartesian product of thus sets. What I fail to see is how we actually define this relation. like if we didn't know what less then meant, and we had to define this relation how would we do it. so if given 2 sets we can compare the elements of the set and systematically determine if an element of one is less than the other?

Asaf Karagila
  • 393,674
CatsOnAir
  • 87
  • 2
    The $<$ relation is just ${(x, y) \in \mathbb{N} \mid x < y}$. Of course, we need a more basic definition of $<$, but we generally assume $<$ to be given or axiomatised. We can define the statement $x < y$ as shorthand for $\exists z \in \mathbb{N} (x + z + 1 = y)$. – Mark Saving Nov 01 '21 at 20:50
  • So if I took the NxN and defined R = {(x,y)| x ∈ N & y ∈ N & ∃z ∈ N(x+z+1=y)} and evaluated 5R6 it would be true for (5,6) ∈ R – CatsOnAir Nov 01 '21 at 22:54

0 Answers0