Path: news.eternal-september.org!eternal-september.org!news.eternal-september.org!feeder2.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Fri, 1 Nov 2024 20:55:27 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <652351709e794674c592b5f246a2a7e1f7867a4a@i2pn2.org>
References: <vb4rde$22fb4$2@solani.org> <vfg07k$1chpe$1@solani.org>
 <7a1e34df-ffee-4d30-ae8c-2af5bcb1d932@att.net> <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>
 <vfjg9h$3rjvp$2@dont-email.me> <vfkqlr$3fii$1@solani.org>
 <vflgnb$fblp$1@dont-email.me> <vflop8$1fpr2$2@solani.org>
 <e7920520807a00a070c701d5953e4416ce0dfd66@i2pn2.org>
 <vfnpf2$ukv3$1@dont-email.me> <vfns3j$3r5kq$2@i2pn2.org>
 <vfoq1m$14lcd$4@dont-email.me> <vfp9q0$3tqss$3@i2pn2.org>
 <vfq750$1fqil$2@dont-email.me> <vfqfpk$3vms5$2@i2pn2.org>
 <vftjuj$26ql1$2@dont-email.me>
 <30dffbdf129483f7b61e3284d1e7bf2ad2e5ea16@i2pn2.org>
 <vg0f4f$2p50e$2@dont-email.me>
 <9ca97f4a24ae1e3041583265125cf860d2fada11@i2pn2.org>
 <vg2bfl$375p7$1@dont-email.me> <vg2c64$3799e$1@dont-email.me>
 <vg2eju$37aml$1@dont-email.me> <30f7c3c7-606e-4fd6-80d7-a89a41e368e9@att.net>
 <vg33df$3b2rd$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sat, 2 Nov 2024 00:55:27 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="526292"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
X-Spam-Checker-Version: SpamAssassin 4.0.0
In-Reply-To: <vg33df$3b2rd$3@dont-email.me>
Content-Language: en-US

On 11/1/24 1:33 PM, WM wrote:
> On 01.11.2024 16:04, Jim Burns wrote:
> 
>> Here,
>> you say: the smallest exists.
>> That does not pop the smallest into existence.
> 
> I say: All exist. That implies the smallest.

Nope. That if your finite thinking.

When "All" is infinite, it doesn't need to have both ends.

That is your problem.

>>
>> It contracts our discourse to
>> lines which have a smallest.
> 
> Yes.
> 
> The other alternative would consist of variable sets.

No, it means coming to grips of the somewhat non-intuative nature of 
infinity. Since we can never have seen infinity, we don't have a natural 
basis to understand it.

>>> Why?
>>> It is a point on the real line,
>>> well separated from its neighbour.
>>
>> You can contract our discourse to
>> real lines with smallest points,
>> but they will also be
>> real lines without smallest points,
> 
> That happens when Cantor's actual infinity is treated like potential 
> infinity. Best example: Hilberts hotel.
> 
> Regards, WM
> 
> 

No, Hilberts Hotel gives us a way to use the potential infinity that we 
have better able to understand to see the rules of what Actual Infinity 
follows.