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: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 2 Nov 2024 18:50:36 +0100
Organization: A noiseless patient Spider
Lines: 22
Message-ID: <vg5opd$3s1gf$3@dont-email.me>
References: <vb4rde$22fb4$2@solani.org> <vfgil3$38pn6$1@dont-email.me>
 <6a90a2e2-a4fa-4a8d-83e9-2e451fa8dd51@att.net> <vfgqoc$39o4h$2@dont-email.me>
 <acd4aad3-9447-45a9-bafd-f8b93d781827@att.net> <vfj3v0$1e96h$2@solani.org>
 <vflnoq$l02$1@news.muc.de> <vfloff$1fpr2$1@solani.org>
 <vflrt7$h190$3@dont-email.me> <vfnp4e$unin$3@dont-email.me>
 <vfns3o$3r5kq$4@i2pn2.org> <vfoq77$14lcd$5@dont-email.me>
 <vfq6rb$3v4c4$4@i2pn2.org> <vfq7hj$1fqil$3@dont-email.me>
 <c388920e-e951-4b06-a8fc-0eb3e6ea7989@att.net> <vftjeq$26ql1$1@dont-email.me>
 <f19c53f7-2509-4f84-8b1e-c42354aa06b5@att.net> <vfu2vd$29m4j$3@dont-email.me>
 <7def94cc-4a51-4305-8e62-0c5b5f5a6b0a@att.net> <vfve6i$9264$1@solani.org>
 <d1d58306-89c7-4000-9663-ef76f7d0f12b@att.net> <vg0fgh$2ppbe$1@dont-email.me>
 <b7c226f2-91a3-4497-88f2-56df5edaf39c@att.net> <vg0on2$2r78m$1@dont-email.me>
 <2bb9c7a7-4fc9-497a-9f81-caea88dc0d4d@att.net> <vg32t6$3b860$1@dont-email.me>
 <01c88350-8726-4d1f-9c67-ec6dd699ef2d@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sat, 02 Nov 2024 18:50:37 +0100 (CET)
Injection-Info: dont-email.me; posting-host="2f7bdf3e653733b4727fe893b0085bd6";
	logging-data="4064783"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/YauU7nm8uMELz6Sxn0gmATPB3Ou2z0KI="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:bej38xVNZ4VlxZCfU7bxJL3Emf4=
In-Reply-To: <01c88350-8726-4d1f-9c67-ec6dd699ef2d@att.net>
Content-Language: en-US
Bytes: 2409

On 02.11.2024 15:10, Jim Burns wrote:
> On 11/1/2024 1:24 PM, WM wrote:

>> Hence
>> at least ℵ₀ points with
>> ℵ₀ intervals of uncountably many points
>> must be between 0 and x₀.
> 
>> That cannot happen at x₀ = 0.
> 
> No.
> There is no x₀ > 0 which,
>   between it and 0,
>    that does not happen.

Then there is an x₀ where it happens.
x₀ =/= 0

Regards, WM