Surreal arithmetic is much nicer than ordinal arithmetic, it is commutative for example. I've always thought that a surreal number library supporting infinite numbers would be useful. Surreal numbers include ordinals but a lot more, they are the largest totally ordered field.

The only library I know of that supports infinite surreal numbers is CGSuite, you can see its hierarchy here: https://github.com/aaron-siegel/cgsuite/blob/e909ab8bc330e39...