On 16 Jul 2010, at 14:39, pugs-comm...@feather.perl6.nl wrote:
Because all C<Real> types are well-ordered
Oh, they are? Just how are we implementing that? <http://en.wikipedia.org/wiki/Well-order > says that the de facto standard foundations of mathematics are insufficient to define a formula for well-ordering the reals. Even if we just consider arbitrary-precision rationals, what's the least element of C<3 ... { (2 * $^p + 2) / ($^p + 2) }>? This sequence consists of infinitely many rationals in which each element is less than its predecessor yet greater than sqrt(2), so there is no least element under the ≤ ordering. If only C<Real> types were required to have a *total* ordering rather than a *well*-ordering; things would be so much simpler.
-- Minimiscience
