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

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DBatchelo1

Posts: 160
Registered: 12/12/04
Re: Finitely definable reals.
Posted: Jan 15, 2013 12:01 PM
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>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


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1/11/13
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1/18/13
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1/13/13
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DBatchelo1
1/13/13
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1/14/13
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DBatchelo1
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Virgil
1/15/13
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DBatchelo1
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mueckenh@rz.fh-augsburg.de
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Virgil
1/16/13
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mueckenh@rz.fh-augsburg.de
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Virgil
1/17/13
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mueckenh@rz.fh-augsburg.de
1/17/13
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Virgil
1/15/13
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Virgil

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