In article <firstname.lastname@example.org>, email@example.com wrote:
> On Thursday, 13 June 2013 18:24:14 UTC+2, Zeit Geist wrote: > > > I said for each particular q e Q, you must be able to produce a natural > > number m_(1/2) such that at step m(1/2) we have for at least one-half of > > all rationals p, p < q, p is in the natural order. > > Why? > > Why should that be required? Is there some axiom demanding it?
For the same reason that WM requires that any and every union of finite sets have a property that is only required in finite sets. A finite ordered set is necessarily well-ordered. An infinite ordered set need not be well ordered.
Thus an infinite union, thus infinite set, of WM's nested sequence of finite, thus automatically well-ordered, sets of rationals, is NOT necessarily well-ordered. And in fact is not well-ordered.
WM's thinking is again seen to be corrupted by the illusions of his WMytheology.
> > With exactly the same right you could demand that there is an n such that > half of all natural numbers have been attached to rationals.
Makes as much sense as your claim that a property of finite sets must apply to infinite sets because infinite sets are infinite unions of finite sets.
> > Your idea should show you very clearly what a nonsense notion countability > is. That it is nonsensical inside of the wild weird world of your WMytheology only means that your WMytheology is itself nonsensical. --