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Relations

When I first learned the definition of a relation:

Relation is a subset of the Cartesian product X × X.

my reaction was: really? That’s it? That’s enough to define a relation?

Knowing intuitively what relations are, I thought that the mathematical definition has to be super complex since it needs to allow for all sorts of weird relations you can think of. But then I started to think about it… And I realized that it’s like saying: all numbers are interesting. Every subset from X × X has been selected as a subset due to some reason. That reason is this particular relation. In the same way, if all numbers are interesting, there is a particular reason for which this particular number is interesting, (even if that reason is: this number is the smallest non-interesting number!).

Indeed, this definition allows for all sorts of weird relations you can think of. Also those you won’t ever think of! It simply accounts for all possible relations. I think that’s the hidden beauty of that definition :-)