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Topic:
Only for mathematicians!
Replies:
4
Last Post:
Aug 29, 2014 12:41 PM



Virgil
Posts:
10,821
Registered:
6/8/11


Re: Only for mathematicians!
Posted:
Aug 29, 2014 12:31 AM


mueckenh@rz.fhaugsburg.de writes:
> On Thursday, 28 August 2014 21:19:12 UTC+2, Ben Bacarisse wrote: <snip> >> Show a formula involving a bijection from N to Q+ that is true in set >> theory but false in WMaths. > > Take Cantor's bijection. I have assumed it. I have assumed that all > naturals are in it. I have shown that then not all rationals are in > it. Every rational in Q+, the set of POSITIVE rationals, is in it, which is all that Cantor ever claimed.
It only takes a simple modification to include every rational in it: in the wellordering of Q+ given by Cantor, insert 0 as first element and insert each negative rational immediately following its absolute value, and the result is a wellordering of ALL of Q that is orderisomorphic to the previous wellordering of Q+, and thus still bijects orderisomorphically to the standard wellordering of N. At least this works correctly everywhere outside of WM's worthless world of WMytheology.  Virgil "Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)



