3 ms·
As I've written in another comment here, a great example of a number-y field which is not totally ordered is Games ⊂ Surreal Numbers ⊂ ℝ. There you have certain
by shemii 3y ago
As I've written in another comment here, a great example of a number-y field which is not totally ordered is Games ⊂ Surreal Numbers ⊂ ℝ.
There you have certain "numbers" which can can confused with (read incomparable) whole intervals of numbers. Games are really cool :)
- SetTheorist 3y agoYou've got the subset relationships backwards: Reals are a subset of the field of Surreal Numbers which is a subset of the group of Games. (Probably better phrased as embeddings, rather than subsets, but the point remains...) Note that Games do _not_ form a field: there is no general multiplication operation between arbitrary games.