|
|
Re: The Distinguishability argument of the Reals.
Posted:
Jan 5, 2013 6:47 AM
|
|
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".
> 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.
Constructible reals are a subset of nameable reals. (Every
prescription for a construction is a name.) Therefore I do not make an
error.
Regards, WM
|
|
