User blog comment:Vel!/On salad numbers/@comment-5150073-20120912091904/@comment-25418284-20120913192515

Oops, you're right. I meant Knuth's/Conway's surreals, where &omega; / 2 = {0, 1, 2, 3, 4, ...|&omega;, &omega; - 1, &omega; - 2, &omega; - 3, &omega; - 4, ...}. Operations on the surreal numbers are also commutative, but yeah, not on Cantor's ordinals.