On 12 Apr., 09:26, JT <jonas.thornv...@gmail.com> wrote:
> > > > For every terminating fraction of r, Cantor obtains a difference > > > between r and the due terminating fraction of the anti-diagonal d: > > > r_nn =/= d_n. > > > He does not obtain one. He constructs one based on > > syntactic criteria.
Blablabla. He puts d_n =/= r_nn. And he says so. But he forgets about the limit.
> > There is no assumption concerning the convergence > > of partial sums whatsoever.
That's why the argument could survive so long. > > > If WM's statement were to be given credence, the Euclidean > > algorithm of long division could no longer be considered > > as providing a faithful representation of distinct real > > numbers (or rational numbers for that matter). > > 0.333... and so on is not 1/3 in any digit place, only in the > imagination of infinite actual representation, you can do your long > division in infinity that number series will *never* represent 1/3.
Correct. Cantorists have to assume that they will get ready, but in general are not willing (or not able) to recognize what they have to assume.
> Partition of the reals into bases using longdivision is not lossless > to use computer terms. It is 0.333... is an identity now they also > claim 1=1.000... is an identity and it is laughable there is no such > creature. The natural 1 is discete is does not have any decimal > expansion.
But some zeros do not change the numerical value. And nobody can really use more than some.