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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, 16 Oct 2024 20:18:09 -0400
Organization: i2pn2 (i2pn.org)
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On 10/16/24 1:18 PM, WM wrote:
> On 16.10.2024 13:54, Richard Damon wrote:
>> On 10/16/24 4:50 AM, WM wrote:
>>> On 16.10.2024 10:27, WM wrote:
>>>> On 15.10.2024 02:00, Jim Burns wrote:
>>>>
>>>>> So, what is that perfectly reasonable explanation?
>>>>
>>>> There is a general rule not open to further discussion:
>>>> When doubling natural numbers we obtain natural numbers which have 
>>>> not been doubled.
>>>
>>> CORRECTION: When doubling natural numbers we obtain even numbers 
>>> which have not been doubled.
>>
>> But that isn't actually a general rule,
> 
> Of course it is a general rule. Doubling creates larger numbers.
> 
> Regards, WM

But those numbers are still in the set, and all the members of the set 
were doubled, so none of the doubled values got us to a value that 
wasn't doubled.

You can only get your rule if you don't actualy do what you said you did.

This is the problem of thinking of infinite sets as if they were just 
like finite set.

The fact that they don't have an "end" over there breaks some of your 
assumptions.