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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Thu, 24 Oct 2024 12:36:35 -0700
Organization: A noiseless patient Spider
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On 10/24/2024 6:42 AM, WM wrote:
> 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.

Nope. There is no largest fraction.

> 
>> 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
>