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Topic:
? 534 Finis
Replies:
3
Last Post:
Aug 13, 2014 2:48 PM




Re: ? 534 Finis
Posted:
Aug 12, 2014 8:39 PM


mueckenh@rz.fhaugsburg.de writes:
> On Tuesday, 12 August 2014 19:09:30 UTC+2, Ben Bacarisse wrote: >> mueckenh@rz.fhaugsburg.de writes: >> >> > On Monday, 11 August 2014 23:00:36 UTC+2, Zeit Geist wrote: >> > >> >> Is you Conclusion Not "There is No Bijection between N and Q? >> > >> > My conclusion is that all naturals cannot index all rationals. >> >> Can you give an example where two sets do index all of each other? > > Yes, of course. Two finite sets of equal cardinality. > >> If it is possible, in WMaths, for finite sets, and the indexing is >> proved via a onetoone correspondence (a bijection), what is the >> difference between these finite bijections and the infinite ones (like >> those in your book)? > > There is no finished infinity.
You've said this a gazillion times. What you won't say is what this means. Obviously I knew you'd ignore my question as to whether exists x c X: not(x c image(f)) because you've painted your self into a corner with that one, but I did think you might have a go answering the other one:
 Given, say, a bijection between N and the finite string over the Latin  alphabet, can you write some formula that is true for this bijection in  the wrong theory that is set theory, but true in WMaths? (Or vice  versa, of course.) Maybe it is, in fact, the formula above?
but it seems even this is too risky for you to have a go at answering. Could it be that you don't know of any formula about such a bijection that is true in set theory and false in WMaths?
> But as I said already, ask about my proof § 533, in particular what > according to your inpression is not correct acorsing to classical > mathematics there.
I have no problem with the theorem in 533.
 Ben.



