+behave like $1/n$? It sort of feels like surreal numbers constructed via finite
+repetitions of our current process will end up building something vaguely like
+the dyadic rationals.
+
+I think some of our equivalence classes are similar. I suspect that the number
+line maintains symmetry with each generation. Since we have ten equivalence
+classes, an even number, symmetry is broken if none of the equivalence classes
+are similar. In fact, since it appears that $\surreal{-1}{1} \similar
+\surreal{}{}$, I'm sure that our equivalence classes can be collapsed further.
+
+I think I can use Definition \autoref{defi:generation} to start proving some
+surreal number properties inductively.
+
+I'm having a lot of problems inserting generation-n into the numberline
+containing generation-0 to generation-(n-1). Since Axiom
+\autoref{ax:leq-comparison} requires comparing against the number itself rather
+than just comparing the sets which define the number, it's hard to slot a new
+generation's number in. For example, how do I test \surreal{}{-1} and
+\surreal{}{1} without working the existing numberline from both ends? I'm
+tempted to note that no number can contain itself, and that the two sets must
+be `less than on the left' and `greater than on the right' to allow just
+comparing sets and finding the right spot on the numberline by working from
+both directions inward, rather than just left to right. Can I make that both
+rigorous and equivalent to Axiom \autoref{ax:leq-comparison}?