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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Thu, 24 Oct 2024 08:24:04 -0400
Organization: Peripheral Visions
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References: <vb4rde$22fb4$2@solani.org>   <4ce512c0-8196-4923-9a6b-359c25fdfa3a@att.net> <vf3ldc$hgts$2@dont-email.me> <8418a2e3-bba2-43b4-8c77-3e947a270476@att.net> <vf3n5v$i1ai$2@dont-email.me> <vf3r29$ipdp$1@dont-email.me> <vf52gf$sc1t$2@dont-email.me> <d854b742bc974c19b0106fa51222bbb640e2d92d@i2pn2.org> <b2090fd4-8329-4c3c-9698-a1e7697040b1@tha.de> <6c56b6df33cedd35cac468735501d2d89ad19048@i2pn2.org> <vf66uf$128bg$1@dont-email.me> <9e98e573c0368690d336299ab78121c3240aa8e7@i2pn2.org> <vf8bqn$1gqlu$1@dont-email.me> <6310990a57ee5388e4e3a2c280fde00fc1b142ae@i2pn2.org> <vf8nre$1ivt6$3@dont-email.me> <vf8r1h$1jnia$1@dont-email.me> <3834533883e5a9dbc8546bf3eb425f762f2d0ab3@i2pn2.org> <vf9202$1kubs$1@dont-email.me> <c2b705b5e27f7c171e819d13313f11983c052506@i2pn2.org> <vfbdq4$251r2$1@dont-email.me> <6c929080fc639ef2e26217ccd2908b1face54361@i2pn2.org> <vfd8hd$2ire9$1@dont-email.me> <d0133e45dbc5e57f40ba09433fef107a4fa11eee@i2pn2.org> <vfdd07$2k42i$3@dont-email.me>
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WM has brought this to us :
> On 24.10.2024 13:43, Richard Damon wrote:
>> On 10/24/24 6:46 AM, WM wrote:
>>> On 23.10.2024 20:59, joes wrote:
>>>> Am Wed, 23 Oct 2024 20:03:48 +0200 schrieb WM:
>>>>> On 23.10.2024 13:37, Richard Damon wrote:
>>>>>
>>>>>> Your complete set of the Natural Numbers is not complete.
>>>>> I take what is given: the complete set of natural numbers. I double it
>>>>> an get, according to mathematics 2n > n greater numbers than were given
>>>>> to me.
>>>> Every single number is greater than its original, but for every number
>>>> in the mapped set there is a greater one in the former set.
>>>
>>> Impossible since all have been mapped, even the greater ones.
>
>> So why can't you get the needed mapped value, since it is in the set.
>
> It is dark and not a natural number.
>
>> Infinity isn't just some impossibly big number that twice itself is bigger 
>> than itself, that is a property of the FINITE.
>
> That's a property of mathematics, of correct mathematics.
>> 
>> You are just unable to understand the infinite, because you just refuse to 
>> let it be what it is.
>
> The infinite must adhere to correct mathematics. Otherwise it is only 
> matheology, to be believed by believers who despise mathematics.

Your idea of mathematics deserves to be despised. 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| and order doesn't really matter. The 
eight doesn't have to wait for the four, and your swapped Bob is 
*always* in the 'next' room since there is no 'last' room at the 
infinite hotel. Scrooge McDuck gets richer and richer as he goes broke. 
Some things are logical but not intuitive.