> 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)