On Sunday, 3 August 2014 16:51:30 UTC+2, Ben Bacarisse wrote:
> > Sorry, you seem to have overlooked this sentence: Assuming this kind > > > of infinity (finished infinity), you get from set theory the result > > > that all rationals can be enumerated. My proof shows that this is > > > wrong for every n and even in the limit. > > > > No, not overlooked. It's not provable (at least you never show a > proof). > I have proven that all naturals do not index all rationals because all naturals leave infinitely many rationals not indexed. In the eyes of all mathematicians with no matheological indoctrination this is a proof. The attempts of matheologians like ZG claiming "all natural numbers of |N" differs from "all of |N" are so sillythat nobody can take them serious.
Your objection is unfounded as well and therefore is of little weight in mathematics. > > > We all know that there are enumerations of the rationals (in set theory, > not WMaths -- even you know that),
You all are taking the first few numbers for "all". That is rather naive.
> > Instead, you should write out "there is an enumeration of the rationals" > in the language of set theory,
Why? It is well known. No matheologian doubts it. Why should I use the language of monolingual matheologians?
> You tried to do that before -- you believed (don't ask me why)
I don't ask you. I have seen that you cannot understand most things of set theory like actual infinity or the reason for undefinable "real" numbers.
> that your > theorem 533 will do as a statement of not(exists enumeration of Q+).
Would you believe that 60 out of 60 understand?
> That's a non-starter now because you've stated categorically that the > negation of theorem 533 is not provable.
I have explained to you twice that it is provable in set theory from invalid assumptions. > > On the other hand, it's possible that you don't know the difference > between a proof by contradiction in a system assumed to be consistent > and a proof that a system is, itself, contradictory.
A contradition shows that some assumption is invalid.