> The problem with transfinite is that you lose commutatively. Depends on which transfinite algebra you're working with. If you restrict "number" to mean "elem

> The problem with transfinite is that you lose commutatively. Depends on which transfinite algebra you're working with. If you restrict "number" to mean "element of an ordered field" (thus excluding things like the "complex numbers" but matching the usual intuition of how numbers should behave) then you can't include Cantor's ordinals but you can include the Surreal Numbers. Those include infinite ordinals and (due to being a field) have commutative addition and multiplication operations.