The point of set theory isn't just to sit around and twiddle our thumbs about

the various definitions we can heap together. It's to create a basis on which we

can build and study interesting things. A great example of that is something

called a *group*. Once we've built up sets enough to be able to understand a set of values and an operator, we're able to build an amazing deep and interesting construction, called a group.

Back when I started this blog, one of the first topics that I

wrote about was group theory. I was just looking back over that

series of posts, and frankly, they sort of stink. I've leaned a lot about

how to write for a blog in the time since then, and so I'd like to go back

and rewrite it. I've never reposted any of the group theory material, so

it should also be new to most readers.