Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: 2N=E
Date: Wed, 30 Oct 2024 16:27:58 +0100
Organization: A noiseless patient Spider
Lines: 37
Message-ID: <vftj9t$26ql2$1@dont-email.me>
References: <vb4rde$22fb4$2@solani.org>
 <8418a2e3-bba2-43b4-8c77-3e947a270476@att.net> <vf3n5v$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> <351593f2-200c-4df5-a93f-9362b8b2bf91@att.net>
 <vf8qk8$1jkh9$1@dont-email.me> <5b701e07-18aa-42ab-964b-0ca84e1776ca@att.net>
 <fb930b22-7f79-4a10-858d-a1a9faccc9b9@tha.de>
 <e2e906ae-48c5-453b-a38f-94c1ebc9ba6b@att.net> <vfgiqa$38oob$1@dont-email.me>
 <d781add9-cd6b-4fff-9601-111c74f4ae32@att.net> <vfgqa8$39o4h$1@dont-email.me>
 <a45b5e62-4b8c-4428-83ef-8b9bf62d6981@att.net> <vfj3e9$1e96h$1@solani.org>
 <40b398d1-40c5-45e9-8615-1cf437af0185@att.net> <vfoqi1$14lcd$6@dont-email.me>
 <3537899e-e951-4138-b56c-fc76340762b8@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 30 Oct 2024 16:27:57 +0100 (CET)
Injection-Info: dont-email.me; posting-host="8cf8b8bceea99c197a16560c9251dc46";
	logging-data="2321058"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18aohPfR2EN6CowOVnTXMmEIozws4yaipg="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:CZL8rEEdXlMwaTyZSR7F0W5dems=
Content-Language: en-US
In-Reply-To: <3537899e-e951-4138-b56c-fc76340762b8@att.net>
Bytes: 3105

On 29.10.2024 18:19, Jim Burns wrote:
> On 10/28/2024 4:01 PM, WM wrote:

>> Relevant is only that
>> the density in the interval is halved,
>> the number remains,
>> the interval is doubled.
> 
> For each finite ordinal n
> there is a larger finite double n+n
> 
> For each finite double n+n
> there is a larger finite ordinal n+n+1
> 
> The finite ordinal interval and
> the finite double interval are the same.
> 
> 'Infinite' does not mean what you want it to mean.
> 
I have no preference.

If infinity is complete, the we can double all natural numbers with the 
result
(0, ω)*2 = (0, ω*2). The some products are in the interval (ω, ω*2). 
Then your claim concerns only the elements of the potentially infinite 
collection of definable numbers.

If infinity is only potential, then your claim concerns all numbers. 
Reason: When all existing numbers are doubled then larger numbers are 
created but those can be natural numbers because the multiplied first 
set was not complete.

Note: It is impossible that all doubled numbers of an interval are 
elements of this interval. If someone claims this, then he is a fool.

Regards, WM