Re: V

On 3/26/2024 6:11 AM, WM wrote:

Le 26/03/2024 à 04:40, "Chris M. Thomasson" a écrit :

On 3/25/2024 4:23 AM, WM wrote:

Le 24/03/2024 à 22:33, "Chris M. Thomasson" a écrit :

On 3/24/2024 1:20 PM, WM wrote:

Le 24/03/2024 à 21:16, "Chris M. Thomasson" a écrit :

On 3/24/2024 1:13 PM, WM wrote:

Le 24/03/2024 à 21:11, "Chris M. Thomasson" a écrit :
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adding one to infinity = infinity.

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If ℕ is complete no natural number can be added.

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Sigh. You are misunderstanding infinity... I think wrt infinity, when you hear the word "complete", your mind instantly thinks, "finite".

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Can you add a natural number to the set of all natura, numbers?

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ℕ is not finite!

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But it is complete. Sets are complete in ZF.

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I think you are confusing complete with finite. This is not true of ℕ.

 Try to think better. Complete means complete, i.e., no element of ℕ is available to be added to ℕ.

ℕ is all the natural numbers, so adding one to it equals itself.
You keep confusing complete with finite.

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Infinity is not finite...

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But logic has to be observed.

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Right. So any natural number you give me, I can say that plus one.

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And that is also already in ℕ.

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This is why ℕ + 1 = ℕ

 No. ℕ + 1 is undefined.
 Regards, WM