"Albrecht" <email@example.com> wrote in message news:firstname.lastname@example.org... > On Wednesday, October 16, 2013 12:21:34 AM UTC+2, Julio Di Egidio wrote: >> <email@example.com> wrote in message >> news:firstname.lastname@example.org... >> >> > Above you see their widely known formulation of the natural numbers. >> > They >> > did not think about the problem of inclusion monotony, probably because >> > they did not imagine the set in the form of my table. >> >> > 1 >> > 1, 2 >> > 1, 2, 3 >> > ... >> >> The set of natural numbers is the limit of that sequence: >> >> 1: 1 >> 2: 1,2 >> 3: 1,2,3 >> ... >> n: 1,2,3,...,n >> ... >> --- >> w: 1,2,3,...,n,...,___w >> >> For geometric reasons, namely for there being a last index, that >> construction rather demands actual infinities. >> >> In that sense, I should concede you have a point, although that is still >> not >> that actual infinities in mathematics make no sense, in fact on the >> contrary. > > The actual infinity of modern math is a wishing well.
You make no sense, you should rather congratulate me for a construction showing that "necessarily, numbers count themselves".
> First, the elementar principle that a collection with X elements contains > a X-th element is broken for the sake of the glory of some dead and the > comfort of some living mathematicians.
Then you have not even bothered to actually read what I have written.
> And second, the arising problems like the Skolem Paradoxon are downplayed > with some pettyfoggeries. Nobody can prove an antinomy in the system of > ZFC, to date. Okay. But the existence of different infinities remains an > angle of view. It is not a "necessity of thinking". There are not more > reals than naturals in a factual sense.
Okay? Angles of view? Factual sense?? The facts of which world, please?
> In the majority, the defenders of Cantors actual infinity are "religious > warriors" without any credentials, are clueless about the whole issue and > are unable of logical reasoning.