Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 12/2/2024 9:30 PM, Moebius wrote:

Am 03.12.2024 um 01:29 schrieb Chris M. Thomasson:

On 12/2/2024 4:00 PM, Chris M. Thomasson wrote:

On 12/2/2024 3:59 PM, Moebius wrote:

Am 03.12.2024 um 00:58 schrieb Chris M. Thomasson:

On 12/2/2024 3:56 PM, Moebius wrote:

Am 03.12.2024 um 00:51 schrieb Chris M. Thomasson:

On 12/1/2024 9:50 PM, Moebius wrote:

Am 02.12.2024 um 00:11 schrieb Chris M. Thomasson:

On 11/30/2024 3:12 AM, WM wrote:

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Finite initial segment[s]: F(n) = {1, 2, 3, ..., n}    (n e IN).

[...]
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When WM writes:
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{1, 2, 3, ..., n}
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I think he might mean that n is somehow a largest natural number?

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Nope, n here may be any element in IN.

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So if n = 5, the FISON is:
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{ 1, 2, 3, 4, 5 }
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[If} n = 3
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{ 1, 2, 3 }
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Right?

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Right.

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Thank you Moebius. :^)

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So, if n = all_of_the_naturals, then

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No, /n/ has to be a natural number, i.e. an element in IN.

 Ahhhh. Okay with me.
 What about {1, 2, 3, ..., n}, where n is taken to infinity? No limit?