6 ms·
Not a professional mathematician, but you have the benefit of set operations mapping to functions you're familiar with. For example, set union becomes the max
by noam_k 2y ago
Not a professional mathematician, but you have the benefit of set operations mapping to functions you're familiar with.
For example, set union becomes the max function.
- epgui 2y agoThat one is neat, but how do you define addition and multiplication on these structures?
- xanderlewis 2y agoYou use (transfinite, if your ordinals are large enough) recursion! Just define a + 1 to be the successor of a — succ(a) — and then, assuming we’ve defined a + b, define a + (b + 1) := (a + b) + 1 = succ(a + b) (it’s only slightly more complicated for infinite ordinals) You can do a similar thing for multiplication, and exponents, and so on. Technically, you have to use induction to prove that this definition indeed works to define the operations for all ordinals.