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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: Tue, 15 Oct 2024 22:45:13 -0400
Organization: i2pn2 (i2pn.org)
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On 10/14/24 6:31 AM, WM wrote:
> On 12.10.2024 22:47, Richard Damon wrote:
>> On 10/12/24 2:19 PM, WM wrote:
>>> On 11.10.2024 03:38, Richard Damon wrote:
>>>
>>>> The SIZE of the set of natural numbers is infinite, and thus obeys 
>>>> the laws of infinite numbers. An infinite number, which has a finite 
>>>> number, added to, multiplied by, or used as a power, is still that 
>>>> same infinite number. It may seem impossible, but that is the nature 
>>>> of infinite numbers.
>>>
>>> No natural number is infinite. They all obey the law of finite 
>>> numbers. That includes the law that 2n > n.
>>
>> Right, but for any number n that is a natural number 2n is also a 
>> natural number and in the set.
> 
> But not in the set of numbers to be doubled. Half of the doubled numbers 
> are not in that set.
> 
> Regards, WM

Why not?

Remember, the set is infinite, so doesn't have an end to go past.

You are just stuck in finite logic and think that infinite sets act just 
the same, they don't, which is part of what makes them infinite, and not 
just unimaginably enormous, which seems to be your idea of "infinite"