Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Mon, 2 Sep 2024 22:37:02 +0200 Organization: A noiseless patient Spider Lines: 36 Message-ID: References: <0da78c91e9bc2e4dc5de13bd16e4037ceb8bdfd4@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Mon, 02 Sep 2024 22:37:03 +0200 (CEST) Injection-Info: dont-email.me; posting-host="10def7a311c7708c5982e6577f7822b5"; logging-data="3144097"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19Ek/fsk6HqinCc/0kITHROatMKBipl2lo=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:OcaHeOHf5Lhd/6+B4GulDPCmveY= In-Reply-To: <0da78c91e9bc2e4dc5de13bd16e4037ceb8bdfd4@i2pn2.org> Content-Language: en-US Bytes: 2465 On 02.09.2024 19:19, Richard Damon wrote: > On 9/2/24 1:07 PM, WM wrote: >> How many different unit fractions are lessorequal than all unit >> fractions? The correct answer is: one unit fraction. If you claim more >> than one (two or three or infintely many), then these more must be >> equal. But different unit fractions are different and not equal to >> each other. >> >> Another answer is that no unit fraction is lessorequal than all unit >> fractions. That means the function NUF(x) >> Number of UnitFractions between 0 and x > 0 >> with NUF(0) = 0 will never increase but stay at 0. There are no unit >> fractions existing at all. >> >> Therefore there is only the one correct answer given above. >> > Nope, because there does not exist AHY unit fraction that is less than > or equal to ALL Unit fractions, Impossible because then NUF will never increase. Then there are no unit fractions. > as any unit fraction you might claim to > be that one has a unit fraction smaller than itself, so it wasn't the > smallest. Your argument stems from visible unit fractions but becomes invalid in the dark domain. > > The problem with your NUF, is that it is trying to count something from > and uncountable end, one that doesn't actually have an end. The unit fractions end before zero. Regards, WM