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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Wed, 23 Oct 2024 07:37:16 -0400
Organization: i2pn2 (i2pn.org)
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On 10/22/24 12:12 PM, WM wrote:
> On 22.10.2024 18:03, Jim Burns wrote:
>> On 10/22/2024 4:13 AM, WM wrote:
> 
>> ℕ is defined such that
>> n ∈ ℕ  ⇔  ∃{0,1,...,n-1,n}
> 
> Most of all it is an invariable set with all its elements existing and 
> subject to doubling.
> 
>> ∀n ∈ ℕ:  2×n ∈ ℕ
> 
> Not if all elements are existing before multiplication already.
> 
> Regards, WM

IF not, then your actual infinity wasn't actually infinite, and you are 
admitting that you logic is just broken.

Your "actual infinity" seems to be just an unimaginably large value, not 
infinite, as your actual infinity has an end, it has an element without 
a successor, so it isn't the set it claims to be.