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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? (infinitary)
Date: Wed, 16 Oct 2024 09:23:43 +0200
Organization: A noiseless patient Spider
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On 16.10.2024 04:45, Richard Damon wrote:
> 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.

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

But it is complete, and all numbers are doubled such that none remains 
which is greater than all doubled numbers.

Regards, WM