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


On 24 Apr., 23:39, "AMiews" <inva...@invalid.com> wrote: > "WM" <mueck...@rz.fhaugsburg.de> wrote in message > > news:5da061c6f643419da1064909c8b20388@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

