Here's the output of my proofreading algorithm, which runs whenever I read something.

In the section Cardinal arithmetic, you have that the set X×Y is the cartesian product of A and B.

In The extended [positive] real line you have 'with a an infinity element'.

In Hyperreal numbers you have '"the" hypperreal numbers'.

In your footnote to The surreal numbers you have 'some a set of characteristic 0 "infinity kitchen sinks"'.

In Cardinal numbers (again), the words 'set of' should be used one more or at least 4 fewer times.

The world needed this article. I'm so glad you wrote it. It obviously needs to be in a more prominent place, and making it a wiki seems like a good idea.