16 Nov
2012
16 Nov
'12
4:57 a.m.
From: "Huddleston, Scott"
David Wilson asks:
Anyway, I was wondering, does 0.99999... = 1 in the surreal numbers?
That depends on how you map infinite decimals into surreals. For sets of numbers A and B with a<b whenever a in A and b in B, surreal "A | B" is the "simplest" number between A and B. The surreals that have finite sets of reals for A and B are dyadic rationals (including integers). ... A better (IMO) mapping of infinite decimals to surreals is .3333... = {.3, .33, .333, .3333, ...} | {.3+.1, .33+.01, .333+.001, ...}
Let a be 0.33, in A, and let b be 0.3+0.1, in B. a<b does not hold. So "|" is not defined. Phil