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

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Virgil

Posts: 10,821
Registered: 6/8/11
Re: Only for mathematicians!
Posted: Aug 29, 2014 12:31 AM
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mueckenh@rz.fh-augsburg.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 well-ordering 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 well-ordering of ALL of Q that is order-isomorphic
to the previous well-ordering of Q+, and thus still bijects
order-isomorphically to the standard well-ordering 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)



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