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Topic: Matheology § 210
Replies: 24   Last Post: Feb 12, 2013 1:12 PM

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fom

Posts: 1,968
Registered: 12/4/12
Re: Matheology § 210
Posted: Feb 10, 2013 4:10 PM
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On 2/10/2013 3:37 AM, WM wrote:
> On 9 Feb., 22:09, Virgil <vir...@ligriv.com> wrote:
>

>> Does the finiteness of the members of that set establish the finiteness
>> of the set itself?

>
> The finiteness of the natural numbers in combination with the constant
> difference of 1 establishes that the natural numbers are in bijection
> with the initial segments. This together with principle of induction
> implies that the sequence 1, 2, 3, ... has no upper threshold. It is
> potentially infinite, but it is not actually infinite.


Neither yes or no.

But, one has

1) the natural numbers

2) something different from the natural numbers

This *combination* establishes a choice function for
the natural numbers

Hence, infinity is assumed





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