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Re: Mueckenheim's Theorema Egregium
Posted:
Aug 18, 2014 5:11 PM


mueckenh@rz.fhaugsburg.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 AntiDiagonal of a List. >> We have Proof, written in a Finite Number of Steps, that No List of >> Real Numbers Contains its AntiDiagonal. > >> 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.



