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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Wed, 6 Nov 2024 06:46:26 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <d2924f8a7ac16ced3e6c3743949c2c087ef9a19c@i2pn2.org>
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On 11/5/24 11:43 AM, WM wrote:
> On 05.11.2024 04:08, Richard Damon wrote:
>> On 11/4/24 12:24 PM, WM wrote:
>>> On 04.11.2024 13:26, Richard Damon wrote:
>>>
>>>> Yes, we know if you will double them again, as we started with the 
>>>> assumption that we double ALL the number, and any even number will 
>>>> be reached from doubling the number that is one half of it and will 
>>>> be doubled again.
>>>
>>> Please mark the sentence which you suspect to be wrong:
>>>
>>> - All natural numbers exist.
>>> - The even numbers have only half of the substance(*) of the integers.
>>
>> Not a valid statement, as half of infinity is still infinity.
> 
> Substance means number obtained from limit: 1/2, 1/2, 1/2, ... --> 1/2.

So, all you are doing is proving that half of infinity is still 
infinity, and not less than itself.

Finite logic just breaks in the infinite realm.

>>
>>> - Multiplication of all elements of a set does not change the substance.
>>>
>>> (*) For every interval (0, 2n] the number E of even natnumbers is 
>>> half of the number N of natnumbers: E/N = 1/2. For (0, oo] we obtain 
>>> the limit of the sequence 1/2, 1/2, 1/2, ... which is 1/2. This is 
>>> the ratio of the substances or, as Cantor called it, the reality.
>>
>> In other words, your logic can only deal with finite subsets of the 
>> infinite set
> 
> It deals with limits.
> 

But wrongly.

Remember, but that same logic, there is not smallest unit fraction.

> Regards, WM