On 15 Jun., 19:36, Uergil <Uer...@uer.net> wrote: > In article > <a709d9b2-7cd9-4c7c-b9f1-4b07bbb4d...@n5g2000vbb.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 15 Jun., 01:56, Uergil <Uer...@uer.net> wrote: > > > In article > > > <f7304e1b-1ddb-4e44-be50-3ed5d30e3...@d6g2000vbe.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 14 Jun., 21:59, Uergil <Uer...@uer.net> wrote: > > > > > > > > Evidently you misunderstood the question. The question is: > > > > > > > Are there uncountably many real numbers. > > > > > > The answer is a resounding: No. > > > > > > Then lets see WM count them! > > > > > That cannot be done, because they are not available. It is a > > > > potentially infinite set. The completely absurd assumption that all > > > > were "there" (because God knows them) is really ridiculous. > > > > > > > No. It is a gross mistake to assume that the rational numbers could be > > > > > > counted. > > > > > > That depends on one's definition of "counting". > > > > > No, it depends on the correct understanding of limits. > > > > Then WM's definition of 'counting' is grossly different from any > > > standard meaning in mathemtics. > > > > Because by a more standard mathematical definition of counting, the set > > > of rationals not only CAN be counted it frequently HAS BEEN counted. > > > > A Google search for "counting the rationals" came up with 174,000 hits > > > in 0.61 seconds, including: > > > You can do better. Simply try it. > > Number of angels: > > 198.000.000 hits in 0.2 s. > > Except that many of the "counting the rationals" hits include > mathematically valid proofs of the countability of the rationals, i.e. > well-orderings of the rationals that are order-isomorphic to the > standard well-ordering of the naturals. > > Does WM claim that any of those "numberings" of the angels are > mathematically valid?
With absolute certainty they are not less valid than enumerations of the rationals.