7 Oct
2004
7 Oct
'04
6:16 p.m.
I was messing around with different addition rules for the surreal numbers; the simplest one gives all rationals as finite-birthday elements, and the mediant as the sum. This gives rise to the Stern-Brocot tree, thus "Sterreal" numbers. {|} = 1 {1|} = 2 {|1} = 1/2 mediant(A,B) = {A|B} if A<=B, {B|A} if B<=A, A if A=B. 1/A = {1/A_R , 1/A_L}; 1/{}={} I'm pretty sure that true addition and multiplication rules will look rather like Gosper's HAKMEM entry on continued fractions. Has anyone else looked at alternate addition rules for surreals? I didn't see any online. -- Mike Stay staym@clear.net.nz http://www.cs.auckland.ac.nz/~msta039