In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 1 Jan., 19:19, Zuhair <zaljo...@gmail.com> wrote: > > The distinguishability argument is a deep intuitive argument about the > > question of Countability of the reals. It is an argument of mine, it > > claims that the truth is that the reals are countable. However it > > doesn't claim that this truth can be put in a formal proof. > > The distinguishability argument is neither deep nor intuitive. And is > not an argument of yours since you do not even understand its > implications. It is simply the basis of the axiom of extensionality. > How should we distinguish elements if they could not be distinguished? > > we arrive finally at: > > > > FINAL CONCLUSION: > > > > The number of all reals is COUNTABLE. > > Of course this would be the result if "countable" was a sensible > notion.
A set is countable if and only if there is a surjection from the set of naturals to that set.
This definition is perfectly sensible in ZFC even if WM claims that it is not sensible in his WMytheology.
And ZFC is considerably more sensible than WMytheology. --