Date: Apr 25, 2013 4:53 AM
Subject: Re: Matheology § 258

On 24 Apr., 23:39, "AMiews" <> wrote:
> "WM" <> wrote in message
> 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