A calculus of the absurd

17.3 Relations

In life, we often ascribe relationships between things, for example, given two individuals \(A\) and \(B\), we might ask whether \(A\) and \(B\) are mortal enemies (or the more likely case, of whether or not \(A\) and \(B\) are friends works too).

We can try to generalise this concept in set theory and derive some results for all relations.

  • Definition 17.3.1 A relation \(R\) on a set \(A\) is a subset of \(A \times A\).