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

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Posts: 4,165
From: London
Registered: 2/8/08
Re: (infinity) A real story
Posted: Oct 16, 2013 9:08 PM
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"Julio Di Egidio" <> wrote in message
> <> wrote in message

>> 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 well-founded. 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} ?


> 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.

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