In the last several lessons we’ve seen many ways to take two sets and form a new set. The four constructions that we studied were the union, the intersection, the Cartesian product, and the disjoint union. In other words, these are four mathematical structures that we’ve built from the more fundamental structure of sets. There are, of course, several other structures that we could construct, however. I challenge you to come up with some definitions of your own for bringing together two sets to form a new one. Feel free to tell me and the rest of the world about them in the comments section, and don’t be shy!
Once you’ve found one, you’ll have built your very own mathematical structure! All you need to do is make sure the construction is well-defined as a set and we’re good. From there, you can ask questions about it—poke it, prod it, examine it, all with the sharpened blade of logic!