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