Virgil
Posts:
6,993
Registered:
1/6/11


Re: Finitely definable reals.
Posted:
Jan 15, 2013 2:50 PM


In article <47ffaebfbac849f7b4115be62cf4170f@googlegroups.com>, Dick <DBatchelo1@aol.com> wrote:
> >On Monday, January 14, You are right, not all finite strings are > >>meaningful. But all meaningful strings are a subset of all finite >strings. > >That is sufficient to know that all meaningful strings are >countable. > >Regards, WM > All meaningful strings that define real numbers are countable in the sense > that they can be mapped into the integers. However, it is not true that they > are countable in the sense that they can be written in a list. > Suppose that there were some way to lok at a statement and determine that if > it was meaninful or not. Then you could write the meaningful statements in a > list. Statement "Diagonalize the set of numbers defined by this list" is a > meaninful statement that defines a real number; it shhould be on the list! > The simplest way to resolve this paradox is to accept that Vountability ( > mappable to the integers) and countability (writable in a list) are different > concepts. > Dick
I am puzzled by your "Vountability ( mappable to the integers)".
Any nonempty set, however large, can be mapped to any other nonempty set, so your "Vountability" does not seem to do anything, except possibly exclude empty sets. 

