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Topic: Matheology § 400
Replies: 79   Last Post: Dec 1, 2013 4:22 PM

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 LudovicoVan Posts: 3,165 From: London Registered: 2/8/08
Re: Matheology § 400
Posted: Nov 27, 2013 3:10 AM

"Virgil" <virgil@ligriv.com> wrote in message
news:virgil-DBC840.12472425112013@BIGNEWS.USENETMONSTER.COM...
> WM <wolfgang.mueckenheim@hs-augsburg.de> wrote:
>

>> A number is definable by its digits or by its construction rule. The set
>> of
>> definable numbers is closed under all mathematical operations, i.e.,
>> every
>> definable number leads always to other definable numbers. The set of all
>> definable numbers is a subset of the countable set of all finite
>> definitions.

>
> But the set of ALL real numbers is not!
>
> There are domains in mathematics which require the existence of more
> numbers than can be given finite definitions.
>
> The standard definition of the real number field is such a domain.
>
> Individual sets of such numbers can be found but not individual members
> of such sets.

Although, if you will pardon a beginner's question, it sounds true that from
definable numbers and definable operations we just get other definable
numbers, so it would be nice to hear where/how exactly we get to undefinable
numbers, and, indeed, what "undefinable number" means at all.

Julio

Date Subject Author
11/25/13 wolfgang.mueckenheim@hs-augsburg.de
11/25/13 Virgil
11/26/13 wolfgang.mueckenheim@hs-augsburg.de
11/26/13 Michael Klemm
11/26/13 William Elliot
11/26/13 wolfgang.mueckenheim@hs-augsburg.de
11/26/13 Virgil
11/27/13 wolfgang.mueckenheim@hs-augsburg.de
11/27/13 Virgil
11/26/13 Virgil
11/27/13 wolfgang.mueckenheim@hs-augsburg.de
11/27/13 Virgil
11/27/13 wolfgang.mueckenheim@hs-augsburg.de
11/27/13 Virgil
11/27/13 LudovicoVan
11/27/13 Virgil
11/27/13 LudovicoVan
11/27/13 wolfgang.mueckenheim@hs-augsburg.de
11/27/13 fom
11/27/13 wolfgang.mueckenheim@hs-augsburg.de
11/27/13 Virgil
11/27/13 wolfgang.mueckenheim@hs-augsburg.de
11/27/13 Virgil
12/1/13 albrecht
11/27/13 fom
11/28/13 wolfgang.mueckenheim@hs-augsburg.de
11/28/13 Virgil
11/28/13 wolfgang.mueckenheim@hs-augsburg.de
11/28/13 Virgil
11/29/13 wolfgang.mueckenheim@hs-augsburg.de
11/29/13 Virgil
11/29/13 wolfgang.mueckenheim@hs-augsburg.de
11/29/13 Virgil
11/28/13 fom
11/28/13 wolfgang.mueckenheim@hs-augsburg.de
11/28/13 Virgil
11/29/13 wolfgang.mueckenheim@hs-augsburg.de
11/29/13 Tucsondrew@me.com
11/29/13 wolfgang.mueckenheim@hs-augsburg.de
11/29/13 Virgil
11/30/13 wolfgang.mueckenheim@hs-augsburg.de
11/30/13 Virgil
11/30/13 Tucsondrew@me.com
11/30/13 wolfgang.mueckenheim@hs-augsburg.de
11/30/13 Virgil
11/30/13 Virgil
11/30/13 Virgil
11/30/13 Virgil
11/29/13 Virgil
11/29/13 wolfgang.mueckenheim@hs-augsburg.de
11/29/13 Virgil
11/30/13 wolfgang.mueckenheim@hs-augsburg.de
11/30/13 Virgil
11/30/13 Tucsondrew@me.com
11/30/13 Virgil
11/30/13 Virgil
11/30/13 Virgil
12/1/13 Virgil
11/29/13 Virgil
11/29/13 wolfgang.mueckenheim@hs-augsburg.de
11/29/13 Virgil
11/30/13 wolfgang.mueckenheim@hs-augsburg.de
11/30/13 Virgil
11/27/13 fom
11/27/13 fom
11/28/13 wolfgang.mueckenheim@hs-augsburg.de
12/1/13 Virgil
11/27/13 Virgil
11/27/13 wolfgang.mueckenheim@hs-augsburg.de
11/27/13 Virgil
11/27/13 Virgil
11/27/13 wolfgang.mueckenheim@hs-augsburg.de
11/27/13 Virgil
11/27/13 wolfgang.mueckenheim@hs-augsburg.de
11/27/13 Virgil
12/1/13 Virgil