4 ms·
That one is neat, but how do you define addition and multiplication on these structures?
by epgui 2y ago
That 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.