LudovicoVan
Posts:
4,065
From:
London
Registered:
2/8/08


Re: (infinity) A real story
Posted:
Oct 16, 2013 9:08 PM


"Julio Di Egidio" <julio@diegidio.name> wrote in message news:l3kf5h$r3e$1@dontemail.me... > <mueckenh@rz.fhaugsburg.de> wrote in message > news:070c86858bde4ddc9b7193058e60463c@googlegroups.com... > >> 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
If I got it correctly, an objection to that construction was that such ordinals are not wellfounded. But, if it is not too basic to ask, what exactly is the problem with an ordinal corresponding to the maximal element of each entry in that increasing sequence, i.e. with n := {m<=n} ?
Julio
> 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.

