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From: joes <noreply@example.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Sat, 27 Jul 2024 12:48:59 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 27 Jul 2024 12:16:24 +0000 schrieb WM:
> Le 27/07/2024 à 13:27, Richard Damon a écrit :
>> On 7/27/24 7:13 AM, WM wrote:
>>> Le 27/07/2024 à 04:23, Richard Damon a écrit :
>>> 
>>>> By your logic, if you take a set and replace every element with a
>>>> number that is twice that value, it would by the rule of construction
>>>> say they must be the same size.
>>> 
>>> That is true in potential infinity. But I assume actual infinity.
>>>>
>> So, what part is not true?
> In potential infinity there is no ω.
Neither is there in actual infinity.

>> Are you stating that replacing every element with another unique
>> distinct element something that make the set change size?
Yes they are.
> In actual infinity the number of elements of any infinite set is fixed.
> Doubling all elements of the set ℕ U ω = {2, 4, 6, ..., ω} yields the
> set {2, 4, 6, ..., ω, ω+2, ω+4, ..., ω*2}.
I wonder how you get the second infinity. What is the preimage of all
the omegas?

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.