Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Mon, 04 Nov 2024 03:35:55 -0500
Organization: Peripheral Visions
Lines: 40
Message-ID: <vga11e$s666$1@dont-email.me>
References: <vb4rde$22fb4$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> <vg2hr4$388sl$1@dont-email.me> <vg31kv$3av1t$1@dont-email.me> <6ed3abd1b4d30ed6db4b9152f7a0ad5da583f147@i2pn2.org> <vg5ame$3qfvj$1@dont-email.me> <vg5o9n$3sb7d$6@dont-email.me> <1acb1cd703640f9df3051921fc01de139f9bc5c5@i2pn2.org> <vg666n$3v6en$3@dont-email.me> <0eb1a655c8044fa2bd8be725442aa04d652eb784@i2pn2.org> <vg8uhg$ik8k$4@dont-email.me>
Reply-To: erratic.howard@gmail.com
MIME-Version: 1.0
Content-Type: text/plain; charset="iso-8859-15"; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 04 Nov 2024 09:35:59 +0100 (CET)
Injection-Info: dont-email.me; posting-host="25012beb60c213514f8614ecd0876d5d";
	logging-data="923846"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19MmC1H+QDg27wZ3C9RNDwWLMwun0O8QIY="
Cancel-Lock: sha1:3AsT7eQOqG4tR2oJU311t6C2hqg=
X-ICQ: 1701145376
X-Newsreader: MesNews/1.08.06.00-gb
Bytes: 3838

Chris M. Thomasson submitted this idea :
> On 11/3/2024 6:34 AM, joes wrote:
>> Am Sat, 02 Nov 2024 22:39:36 +0100 schrieb WM:
>>> On 02.11.2024 21:34, Richard Damon wrote:
>>>> On 11/2/24 1:42 PM, WM wrote:
>>>>> On 02.11.2024 14:50, Moebius wrote:
>>>>>> Am 02.11.2024 um 14:21 schrieb joes:
>>>>>>> Am Fri, 01 Nov 2024 18:03:26 +0100 schrieb WM:
>>>>>>
>>>>>>>> If an invariable set of numbers is there, then there is a smallest
>>>>>>>> and a largest number of those which are existing.
>>>>>> or each and every n e IN there is an n' e IN (say n' = n+1)
>>>>> Actual infinity is not based on claims for each and every, but
>>>>> concerns all.
>>>> But if it applies to ALL, it must apply to ANY, so a property of ANY
>>>> must apply to each on of the ALL.
>>>> So, for ALL the Natural Numbers, there can't be a highest, because for
>>>> ANY Natural Number there is a following one
>>> That cannot be true for all dark numbers.
>> And that is why "dark" numbers are not natural (or the naturals are all
>> not dark).
>> 
>
> Well, what if the dark numbers are natural wrt:
>
> 1, 2, 3, 4, ...
>
> Oh shit! WM says ... is dark. I say 5, then WM says well okay 5 is not dark 
> now. Shit like that? Its rather hilarious to me.

It may make more sense to go higher. Consider the 123^456^789th prime 
number. I would be pairing the natural number 123^456^789 with some 
really large prime number. Which prime? I don't know. WM eschews such a 
pairing because the value of that prime is unknown, or 'dark' and he 
thinks it cannot be used in a pairing.

Had I been matching instead of pairing, he would have a point because 
it would likely be impossible for me to check that the 123^456^789th 
prime has the correct natural number index. For pairing, I don't need 
the values, only the countability, but for matching I might.