On Monday, 18 August 2014 23:05:00 UTC+2, Ben Bacarisse wrote:
> You agree that, given S(q) = 1 / (2 floor(q) - r + 1) and B(n) = S^n(1),
I agree that many bijections |N <--> Q+ have been defined.
> Q+ = image(B) > > B(p) = B(q) iff p = q > > for all n c N, exists q c Q+, q = B(n) > > > > > More is not intended. > > > > More than the above is not required.
In fact, in potential infinity more is nor required. But if actual infinity is assumed, then infinite sets can be exhausted. Then |N is exhausted before Q+.
This kind of infinity is required for Cantor's diagonal argument and for his "proof" of transcendental numbers.
His assuming of the complete set |N is identical with my assuming of the complete set |N. There is no rational argument denying my argument but accepting Cantor's. See the desparate attempts by YMB, ZeitGeist and others. You say you accept my result (and there you are the only correct one) but you deny to draw the consequences.