In article <firstname.lastname@example.org>, email@example.com wrote:
> > Then behave and write like a civilized person!
That from WM is a laugh, as WM neither behaves nor writes at all like civilized person.
> > Read what is written, not what want to read.
Advice that WM often gives but never follows,
> > That shows that by adding rationals one by one it is impossible to exhaust > all of them. Therefore countability is a nonsense notion.
Then, equally, no infinite sequence can have a limit. > > > The rationals and the naturals are NOT order isomorphic. > > Neither they are equinumerous.
The rationals and the naturals are well known to be bijectable, which everywhere outside of the wild weird world of WMytheology translates to equinmerous. > > > Also, I'm sure, whatever proof this is from, it's about Cardinals and not > > Ordinals. Do you know the difference? > > > > That does not play a role in a case where we only have to show that every > enumerated rational eventually will be taken into the well-ordered set.
WM is claiming that the union of an increasing sequence of sets will have any property common to all those sets, and thus, since an increasing set of ordered but finite, thus well-ordered, sets of rationals will union to the set of all rationals, the set of all rationals in natural order must be well-ordered.
But according to that same argument, WM is claiming that because all those sets of rationals are finite that their union, the set of all rationals must also be finite.
So we can easily see that WM's main thesis, the assumption that a limit must have all the properties common to all the members of the sequence of which it is the limit, only holds in the the wild weird world of WMytheology.
Outside of the wild, weird world of WMytheology, (1) infinite sequences are actually infinite as sets, (2) infinite sets are actually infinite, (3) an infinite union of finite sets need not be finite, (4) an infinite union of well-ordered sets need not be well-ordered, (5) an infinite union of FISONs need not be a FISON, and WM just does not understand how proper math works. --