Path: ...!eternal-september.org!feeder2.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: Sat, 2 Nov 2024 13:22:19 -0700 Organization: A noiseless patient Spider Lines: 59 Message-ID: References: <30dffbdf129483f7b61e3284d1e7bf2ad2e5ea16@i2pn2.org> <9ca97f4a24ae1e3041583265125cf860d2fada11@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 02 Nov 2024 21:22:21 +0100 (CET) Injection-Info: dont-email.me; posting-host="6e8fcc6cbd8587a7e26447d4479abcfd"; logging-data="4150047"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/WXA3RxB81gqTkOM4f8Bx1EDaIpdxRwLs=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:FuBXoQkYqN6tcVB6aHrnDlxDybQ= In-Reply-To: Content-Language: en-US Bytes: 4257 On 11/2/2024 11:03 AM, Ross Finlayson wrote: > On 11/02/2024 06:54 AM, FromTheRafters wrote: >> WM was thinking very hard : >>> On 01.11.2024 22:53, FromTheRafters wrote: >>>> WM explained on 11/1/2024 : >>>>> On 01.11.2024 19:39, FromTheRafters wrote: >>>>>> WM formulated the question : >>>>> >>>>>>>> Infinite subsets don't do that for you, even if you wish really >>>>>>>> hard. >>>>>>> >>>>>>> They cannot evade if they are invariable. >>>>>> >>>>>> Sets don't change. >>>>> >>>>> Therefore the elements do not depend on us and our knowledge. "If I >>>>> find x, then I can find x + 1" is not relevant. "For every x (that I >>>>> find) there is x + 1" is no relevant. All elements are there, >>>>> independent of what we know or do. Therefore the first and the last >>>>> are also there independent of us. If they weren't, their existence >>>>> would depend on some circumstances and could change. >>>> >>>> Circumstances like "there is no last element"? >>> >>> That means, there is always another element. Potential infinity. >> >> Sets don't change. Forget about amplifying 'not finite' with such as >> 'actual' and potential' -- infinite simply means not finite and >> 'actual/potential' is a distinction without a difference. A useless >> concept outside of math philosophy. >> >>>> the set of denominators have no largest element to 'start' with. >>> >>> If all unit fractions are existing, then a smallest unit fraction is >>> existing. If NUF(x) has grown to ℵ₀ at x₀, then ℵ₀ unit fractions must >>> be between 0 and x₀. Hence at least ℵ₀ points with ℵ₀ intervals of >>> uncountably many points must be between 0 and x₀. That cannot happen >>> at x₀ = 0. >>> >>> Is that too hard to understand? >> >> Apparently, for you. > > Au contraire, there are multiple law(s) of large numbers, What about this sucker (42^999429994299942) * 2 ? Oh, don't forget about ((42^999429994299942) * 2) + 1 damn it! > and in mathematics like emergence after convergence, > the potential / practical / effective / actual distinction, > of "infinity", is a thing. > > You know who discovered mathematics? Philosophers. > >