Comment on nooo my genderinos
homura1650@lemmy.world 5 days agoI was going to make a comment about surreal numbers not being numbers. But I did a bit of fact checking and it looks like all of the values I was objecting to are not considered surreal numbers, but rather pseudo numbers.
I find this outrageous. Why can’t ↑ be a number? What even is a number that would exclude it and leave in all of your so-called numbers?
Inucune@lemmy.world 4 days ago
Axioms. en.m.wikipedia.org/wiki/List_of_axioms
homura1650@lemmy.world 4 days ago
Where in those axioms does it say that ↑ = {0|∗} = {0 | {0|0} } is not a number? No where, that’s where!
The actual reason that ↑ is simply that it is too ill behaved. The stuff I thought were the “numbers” of combinatorical game are actually just called Conway games. Conway numbers are defined very almost identically to Conway games, but with an added constraint that makes them a much better behaved subset of Conway games.
I suppose you could call this an axiom of combinatorical game theory; but at that point you are essentially just calling every definition an axiom.
<s> Getting back to my original point; this distinction just goes to show how small minded mathematicians are! Under Conway’s supposed “reasonable” definition of a number, nimbers are merely games, not proper numbers. However, the nimbers are a perfectly good infinite field of characteristic 2. You can’t seriously expect me to believe that those are not numbers! </s>