# I Like Abstract Things: Summary

Okay, so you're a dreamer. There's plenty in algebra for you, too. Just think: we've touched on the concept of infinity, which is pretty far out there. Even if you were immortal (you're not), you couldn't finish reading the decimal representation of a single irrational number. Plus, there are so many irrational numbers that you can't possibly list them all. However, we can list all the *rational* numbers, which means that, although there are infinitely many rational numbers, there are still more irrational numbers than rational numbers.

Mind. Blown.

These ideas are part of set theory, which addresses what it means to "count" collections of infinitely many objects. (You know, like Jay Leno's car collection.)

We've also started proving theorems, such as the fact that the square root of 2 is irrational. Most of mathematics is more about proofs than about arithmetic, but arithmetic is a good place to find some interesting proofs. So is a photography studio, come to think of it.

Let's continue on to Algebraic Expressions!