Re: 2N=E

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