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Topic: Finitely definable reals.
Replies: 52   Last Post: Jan 18, 2013 2:37 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Finitely definable reals.
Posted: Jan 15, 2013 2:50 PM

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.
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