LudovicoVan
Posts:
3,815
From:
London
Registered:
2/8/08
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Re: (infinity) A real story
Posted:
Oct 15, 2013 6:21 PM
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<mueckenh@rz.fh-augsburg.de> wrote in message
news:070c8685-8bde-4ddc-9b71-93058e60463c@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
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