Each surreal number is constructed with a set of surreals to the left and right, so each such construction has a left and right set, not merely a left and right number. So, in the equation { 0 | 1 } = 1/2, the expression on the left side means a surreal whose left set is {0} and whose right set is {1}. The left and right sets can be infinite, otherwise we would never be able to construct infinitesimals, or even 1/3, for that matter. On Fri, Nov 16, 2012 at 2:12 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I missed the first post, but: I thought surreals were constructed with a surreal on the left and a surreal on the right.
So what does it mean to have a sequence on the left and/or right? I might be able to guess, but would rather know how (and where) this is defined.
Thanks,
Dan
On 2012-11-15, at 9:39 PM, Huddleston, Scott wrote:
Minor correction: I said {.3, .33, .333, .3333, ...} | {} is 1/2 in the surreals. Actually, it is 1. Still reinforcing that
{.3, .33, .333, .3333, ...} | {.3+.1, .33+.01, .333+.001, ...} = 1/3 Is the better way to map infinite decimals into surreals.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun