Path: ...!npeer.as286.net!npeer-ng0.as286.net!3.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Date: Mon, 7 Oct 2024 17:35:50 -0700 Organization: A noiseless patient Spider Lines: 53 Message-ID: References: <05a3027798506434bf2f30b527e0f57d300e76c3@i2pn2.org> <6f188d193341a3862f4c788a44dff3dfb27fb6bd@i2pn2.org> <81f6f0271a53803c0bf79be304ce2484e33aecda@i2pn2.org> <7403c9bb7e2d0ac17197c219c6a04eace8fef108@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 08 Oct 2024 02:35:52 +0200 (CEST) Injection-Info: dont-email.me; posting-host="d938895af8a55dcdf6009a32333c8ef4"; logging-data="2011100"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19r1x9Tse8v5pHwrBpNG8oGXvmnUjfzyIg=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:R541mQGopDDqBndWQB2Z4FP2m0c= Content-Language: en-US In-Reply-To: <7403c9bb7e2d0ac17197c219c6a04eace8fef108@i2pn2.org> Bytes: 4087 On 10/7/2024 3:58 PM, Richard Damon wrote: > On 10/7/24 7:44 AM, Alan Mackenzie wrote: >> Richard Damon wrote: >>> On 10/7/24 7:13 AM, joes wrote: >>>> Am Mon, 07 Oct 2024 10:13:21 +0200 schrieb WM: >>>>> On 06.10.2024 17:55, joes wrote: >>>>>> Am Sun, 06 Oct 2024 17:26:07 +0200 schrieb WM: >>>>>>> On 06.10.2024 16:52, Alan Mackenzie wrote: >>>>>>>> WM wrote: >> >>>>>>>> This idea of time may be what misleads the mathematically less >>>>>>>> adept >>>>>>>> into believing that 0.999... < 1. >>>>>>> That is true even in actual infinity. >>>>>>> We can add 9 to 0.999...999 to obtain 9.999...999. But multiplying >>>>>>> 0.999...999 by 10 or, what is the same, shifting the digits 9 by one >>>>>>> step to the left-hand side, does not increase their number but >>>>>>> leaves >>>>>>> it constant: 9.99...9990. >>>>>>> 10*0.999...999 = 9.99...9990 = 9 + 0.99...9990 < 9 + 0.999...999 ==> >>>>>>> 9*0.999...999 < 9 as it should be. >>>>>> In actual infinity, there is no last 9 (that would not be infinite). >>>>> Actual means all, but not more. This implies a last before ω. The >>>>> infinity means an end cannot be determined. It is produced by the dark >>>>> numbers. >>>> Actually infinite means infinite, which doesn’t change when you add or >>>> subtract a finite number. >> >> >>> Actual infinity doesn't exist for us finite beings. >> >> English language tip: The "Actually" in that sentence was not attached to >> the word "infinite", it meant something like "This is really true:". > > But all his reference to the word "Actually" are part of his trying to > define the term "Actual Infinity". > >> >> Anyhow, what do you mean when you say that "actual infinity doesn't >> exist"?  I think we established over the weekend that for a mathematical >> entity not to exist, it must cause a contradiction.  Or something like >> that. >> >> So what contradiction would the existence of actual infinity cause? >> > > It implies that there exists a first positive real, rational number or > unit fraction for one (at least the way WM uses it). A first unit fraction would be 1/1? :^) However this is in the very _strict_ realm of unit fractions. WM seems to like to mix and match realms. Not sure why he thinks there is a smallest unit fraction... Anyway, shit happens.