LudovicoVan
Posts:
3,815
From:
London
Registered:
2/8/08


Re: (infinity) A real story
Posted:
Oct 15, 2013 6:21 PM


<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
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.
Julio

