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Topic: Mueckenheim's Theorema Egregium
Replies: 3   Last Post: Aug 19, 2014 12:13 PM

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Ben Bacarisse

Posts: 1,254
Registered: 7/4/07
Re: Mueckenheim's Theorema Egregium
Posted: Aug 18, 2014 5:11 PM
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mueckenh@rz.fh-augsburg.de writes:

> On Monday, 18 August 2014 21:20:21 UTC+2, Zeit Geist wrote:
<snip>
>> We have a Finite Definition for "Complete Ordered Field".
>> We Assume the Set of Real Numbers is a Complete Ordered Field.
>> We have a FInite Definition of Decimal Sequence.
>> We Prove Every Decimal Sequence Represents a Real Number, and vice versa.
>> We have a Finite Definition of Countability.
>> We have a Finite Definition of a List of Real Number.
>> We have a Finite Definition of an Anti-Diagonal of a List.
>> We have Proof, written in a Finite Number of Steps, that No List of
>> Real Numbers Contains its Anti-Diagonal.

>
>> What's the Problem?
>
> All finite definitions belong to a set that is not uncountable.


From your book:

Die Menge der rationalen Zahlen ist Q = { m/n | m e Z /\ n e N }
Die Menge der reellen Zahlen ist R = { x | x besitzt eine Dezimaldarstellung }

If the decimals must all be finite, Q = R.

--
Ben.



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