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Topic: (infinity) A real story
Replies: 9   Last Post: Oct 16, 2013 9:08 PM

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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
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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