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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Fri, 4 Oct 2024 11:33:02 +0200
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On 04.10.2024 10:11, joes wrote:
> Am Thu, 03 Oct 2024 20:31:41 +0200 schrieb WM:
>> On 02.10.2024 23:06, Jim Burns wrote:
>>> On 10/2/2024 7:10 AM, WM wrote:
>>
>>> You (WM) believe in quantifier shifts,
>>> the opposite of that.
>> I believe that if every n that can be chosen has ℵ₀ successors, then all
>> n that can be chosen have ℵ₀ successors. Proof by your inability to
>> contradict this.
> That is not the same thing, but an invalid deduction.

It is fact. What you believe valid or invalid is not of interest to me. 
I know that all numbers which you can choose have ℵ₀ successors. 
Therefore the collection containing all numbers which you can choose has 
ℵ₀ successors.
>>>> 1, 2, 3, ..., ω-2, ω-1, ω
>>> ...is a _finite_ sequence.
>>> As you have written it,
>>> ω and each non.0 α < ω has a predecessor,
>>> which makes ω finite.
>> The predecessors in the dark realm cannot be known. You can subtract
>> every natural number from ω without traversing the dark realm. You can
>> add every natural number to every natural number without traversing the
>> dark realm. That is the essence of infinity!
> No, the infinity is at the end, not in the middle.

A common misbelief about actual infinity based on potential infinity.

Regards, WM