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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Mon, 4 Nov 2024 22:08:46 -0500
Organization: i2pn2 (i2pn.org)
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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.

> - 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, and thus isn't a system that can handle actual infinity.

> 
> Regards, WM