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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Tue, 8 Oct 2024 12:55:31 -0700
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On 10/8/2024 5:35 AM, Richard Damon wrote:
> On 10/8/24 5:54 AM, WM wrote:
>> On 07.10.2024 15:19, Alan Mackenzie wrote:
>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>
>>>> No, even an unbounded sequence does not get longer when shifted by 
>>>> one step.
>>>
>>> The concept of "length" appropriate for finite sets doesn't apply to
>>> infinite sets.
>>
>> It is the concept of number of elements. It is appropriate in actual 
>> infinity.
> 
> Which has been shown to not exist for us finite beings, as it is too big 
> for us to see.
> 
>>
>>> infinite means "without end" - unendlich.
>>
>> Actual infinity means complete. That implies a fixed number.
> 
> Which has been shown to not exist for us finite beings, as it is too big 
> for us to see.
> 
>>>> You don't understand that actual infinity is a fixed quantity.
>>>
>>> It may be "fixed" whatever that might mean, but to regard it as a
>>> "quantity" is more than questionable.
>>
>> Fixed means that no element can be added and no element can be lost. 
>> The number of nines is fixed. That is an assumption only, but 
>> necessary for bijections.
> 
> Yes, it is fixed, at INFINITY, which means there is no end to it, and 
> thus we can't add a zero "at the end" which doesn't exist.
> 
> This is why finite beings can't use "actual infinity" because it is too 
> big for us to handle.

Ummm... Well, not sure what to think about that. Hummm... Any time you 
use a number it is in actual infinity. Think of the number four. It is 
in a pool of the infinitely many natural numbers, and we just used it...

Fair enough, or weasel words?