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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: Wed, 16 Oct 2024 11:04:37 -0700
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On 10/16/2024 9:58 AM, WM wrote:
> On 16.10.2024 18:09, FromTheRafters wrote:
>> WM formulated on Wednesday :
>>> On 16.10.2024 13:54, Richard Damon wrote:
>>>> On 10/16/24 4:30 AM, WM wrote:
>>>
>>>>> There is a general rule not open to further discussion:
>>>>> When doubling natural numbers we obtain even numbers which have not 
>>>>> been doubled.
>>>>> In potential infinity we obtain more even numbers than have been 
>>>>> doubled.
>>>>> In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.
>>>>>
>>>> But that isn't actually a general rule,
>>>
>>> It is a general rule that doubling creates larger numbers.
>>
>> It is a general rule that doubling finite cardinal numbers creates 
>> larger finite cardinal numbers.
> 
> Yes.
> 
>> In transfinite cardinalities Aleph_Zero times two is still Aleph_zero 
>> though.
> 
> Here we talk only about natural numbers to be doubled.

1*2=2
2*2=4
3*2=6
4*2=8
....

2, 4, 6, 8, ...

All natural numbers can be doubled, and they result in a natural number. 
Got it? It's simple.