Date: Apr 25, 2013 4:53 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 258

On 24 Apr., 23:39, "AMiews" <inva...@invalid.com> wrote:
> "WM" <mueck...@rz.fh-augsburg.de> wrote in message
>
> news:5da061c6-f643-419d-a106-4909c8b20388@a34g2000vbt.googlegroups.com...
> Matheology § 258
>

> > Irrationals are not real
>
> e is a real number, so is Pi.
>

> > {{ - at least they have no real strings of digits,
>
> they are represented by strings of real digits,


Nobody can read, write or use an infinite string.
Real numbers are represented by *finite names* that allow to
*calculate a rational approximation up to any desired digit*. This is
generally called a potentially infinite sequence (of approximations)
and often mistaken as an infinite sequence. But it is not the same as
an actually infinite string that defines, by sequence of digits, a
real number without doubt.

No string of digits, without a finite formula to generate it, defines
an irrational number.
>
> > and only countably many of them can be defined in a language that can be
> > spoken, learned and understood}}.

>
> have you counted them ?  How many are there ?


Not more than aleph_0

Regards, WM