>it includes lots of numbers that are extremely difficult to describe We'd have to describe them in order to set a rule's power to that.
>arguably, weirdo numbers like... the surreal numbers Arguably. Besides, this proposal isn't going to automatically add 3i to every rule's power; there's still the matter of passing proposals as a check. >Meanwhile, the rational numbers have the convenient property that every >countable totally ordered set is order-isomorphic to a subset of the rational >numbers. I don't think this is terribly relevant for any irrational numbers we can actually describe. On Mon, Jul 22, 2013 at 12:47 PM, Tanner Swett <swe...@mail.gvsu.edu> wrote: > On Jul 22, 2013, at 1:51 AM, James Beirne wrote: >> Proposal: Π & Co.: >> >> Remove the word "rational" from rule 1688. > > Why would we want to do that? The set of all non-negative numbers is pretty > nebulous; it includes lots of numbers that are extremely difficult to > describe, or not possible to define in finitely many symbols, along with, > arguably, weirdo numbers like the ordinal numbers, the cardinal numbers, the > complex numbers, the split-complex numbers, the dual numbers, and the surreal > numbers. Meanwhile, the rational numbers have the convenient property that > every countable totally ordered set is order-isomorphic to a subset of the > rational numbers. > > --Machiavelli
