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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Tue, 5 Nov 2024 17:43:12 +0100
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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.
> 
>> - 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.

Regards, WM