Virgil
Posts:
6,613
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 5, 2013 5:22 PM
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In article
<bb7be2f4-a0c3-4538-baf6-527a064d1771@b8g2000yqh.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 4 Jan., 19:47, fom <fomJ...@nyms.net> wrote:
> > The rationals
> > are not complete. So much so, in fact, that they are a set
> > of measure zero.
> >
> > But, wait.
>
> No reasonable reason to wait. "Measure zero" is a nonsense expression
> because it presupposes aleph_0 as a meaningful notion. There are
> convergent sequences, but the limit is never assumed, not "after
> aleph_0 steps".
So WM would throw out all of measure theory with his bathwater.
>
> > A set of measure zero presumes a sigma algebra generated
> > from the open sets of the topology (or the compact sets if you
> > prefer).
> >
> >
> >
> > > Cantor's list establishes the uncountability of distinguishable and
> > > hence constructable reals.
> >
> > Constructible real has a definite sense that you
> > do not abide by. You should talk of nameable reals and
> > Frege's notion of definite symbols.
WM should not talk at all, since he would throw out so much of standard
mathematics in order to keep his WMytheology "pure".
>
> Constructible reals are a subset of nameable reals. (Every
> prescription for a construction is a name.) Therefore I do not make an
> error.
Non-Sequitur. It is plainly obvious to everyone except WM that he makes
errors all the time, and then squirms wildly to cover his ass.
>
> Regards, WM
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