Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
§ 534 Finis
Replies:
8
Last Post:
Aug 14, 2014 1:33 PM




Re: § 534 Finis
Posted:
Aug 13, 2014 3:45 PM


mueckenh@rz.fhaugsburg.de writes:
> On Wednesday, 13 August 2014 00:53:41 UTC+2, Ben Bacarisse wrote: > >> > Could you please let us know what in the proof of § 533 deviates from >> > classical mathematics or at least mathematics as you understand it?
Why did you not answer the point I raised, having invited it in the first place? Is it because you can't? Your post "deviates from classical mathematics" by not making use of the fact that
exists x c Q+: not(x c image(b))
is false as a direct consequence of facts you have already agreed to. Why pretend to care what people think, when you have no intention of answering the tough questions?
>> As I've said before, I have not problem with the theorem >> in 533. > > Because you don't understand its implications: All natural numbers are > shown to leave infinitely many rationals without index in Cantor's > asserted complete bijection.
How curious that you can't write that out as a theorem, but instead have to imply it:
"Everybody may impartially examine himself whether he is willing to believe that nevertheless all rational numbers can be enumerated."
Why did you not prove the theorem that you really want: all rationals can not be enumerated? That's easy to answer: because you can't write it out without letting people know what you mean (or, possibly, because you can't write it out at all). You have to prove a rather trivial theorem instead, and invite people to speculate on the implications where in fact there are none.
 Ben.



