In article <firstname.lastname@example.org>, 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 non-empty set, however large, can be mapped to any other non-empty set, so your "Vountability" does not seem to do anything, except possibly exclude empty sets. --