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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Thu, 24 Oct 2024 15:42:55 +0200
Organization: A noiseless patient Spider
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On 24.10.2024 14:24, FromTheRafters wrote:
> WM has brought this to us :

>> The infinite must adhere to correct mathematics. Otherwise it is only 
>> matheology, to be believed by believers who despise mathematics.
> 
> Sets don't change. If 
> you want to double each element of the naturally ordered set of natural 
> numbers you do it by creating another set with the naturally ordered 
> doubled elements.
> 
> {1,2,3,4,...}
> {2,4,6,8,...}
> 
> These sets are the same |size|

In fact, here "the same size" applies. The change of size between both 
sets is +/- 0. But since the first set contains all natural numbers, the 
second set contains larger numbers because 2 > n.

> your swapped Bob is 
> *always* in the 'next' room since there is no 'last' room at the 
> infinite hotel.

But if all fractions can be counted, then there is a last state, namely 
when this is counting is complete.

> Scrooge McDuck gets richer and richer as he goes broke.

He does never lose more money than he gets. Therefore he cannot lose all 
his money. *That* is dictated by logic.

Regards, WM