Large Countable Ordinals (Part 1)

I love the infinite.

It may not exist in the physical world, but we can set up rules to think about it in consistent ways, and then it’s a helpful concept. The reason is that infinity can be simpler to think about than a very large finite number.

Finding rules to work with the infinite is one of the great triumphs of mathematics. Cantor’s realization that there are different sizes of infinity is truly wondrous—and by now, it’s part of the everyday bread and butter of mathematics.

Trying to cr...