Path: news.eternal-september.org!eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 19 Oct 2024 13:10:20 +0200
Organization: A noiseless patient Spider
Lines: 21
Message-ID: <vf042r$3rmh1$1@dont-email.me>
References: <vb4rde$22fb4$2@solani.org> <ve96jj$38qui$2@dont-email.me>
 <ve97c7$2f64$1@news.muc.de> <ve97qj$38qui$4@dont-email.me>
 <3f5fcf13171337f1c3d2ef84cc149be327648451@i2pn2.org>
 <veecr3$7rap$1@dont-email.me>
 <97b84c07aa526903a0788584f7f7ae9121f8b81f@i2pn2.org>
 <veirkn$desj$2@solani.org>
 <db221d267ae4b956cd0818c9b5ccc0311df97d1e@i2pn2.org>
 <60f1280e-e226-4314-8eca-da5410be8ca3@tha.de>
 <96a7aa944085e76faed69c8db9a8dca599e1a159@i2pn2.org>
 <vejhcb$ditg$1@solani.org>
 <2c732eefb860986209bd46ed88391ddceaddff55@i2pn2.org>
 <vOmcnYVG-OHpKZP6nZ2dnZfqnPSdnZ2d@giganews.com>
 <avecnXK3J6VsU5P6nZ2dnZfqnPhg4p2d@giganews.com>
 <vensvb$2533b$2@dont-email.me> <veoumv$2bc1q$4@dont-email.me>
 <veovbm$2bc2g$2@dont-email.me>
 <aqCcnTFQ7MNz_436nZ2dnZfqnPudnZ2d@giganews.com>
 <bd2fe5d4-c284-47e7-a265-720539d2ab42@att.net>
 <27WcnWnC9tjPyIz6nZ2dnZfqn_idnZ2d@giganews.com>
 <f1e485be-dc79-49ba-87fa-4bb23910d878@att.net>
 <4d080bc4-7c84-4951-a8f4-9bf0f95ad47f@tha.de>
 <dcd6560e-e5cc-4c14-8607-c32977f6c622@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sat, 19 Oct 2024 13:10:19 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="2bfd11be6f346f137431b612c52d5296";
	logging-data="4053537"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+oxkXrvFMJ0GDhlbK0futUGHi5HOyYVeg="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:wkCWw17O/pYpWyc5G5wq8n5MTOw=
In-Reply-To: <dcd6560e-e5cc-4c14-8607-c32977f6c622@att.net>
Content-Language: en-US

On 19.10.2024 12:56, Jim Burns wrote:

> A number immediately before an infinite ordinal
> is an infinite ordinal.

That is the traditional opinion. It has lead to internal contradictions 
(vanishing Bob). Therefore we have to use a new system, free of 
contradictions: Dark numbers.

>> What is immediately before ω
> No number exists immediately before ω

Immediately or not: The number before ω is finite.

> ω-1 can't be infinite and must be infinite.

ω-1 is a natural number, but the dark numbers occupying almost all space 
between 0 and ω act like an infinity. We cannot look or count through 
them although all are finite, alas too large.

Regards, WM