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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Thu, 12 Sep 2024 13:36:08 -0700 Organization: A noiseless patient Spider Lines: 21 Message-ID: <vbvjbq$drip$1@dont-email.me> References: <vb4rde$22fb4$2@solani.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Thu, 12 Sep 2024 22:36:11 +0200 (CEST) Injection-Info: dont-email.me; posting-host="26dfebf598c361779a3e3249a41dbd07"; logging-data="454233"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18rzDtK/UqvsQVoaSWjrnPX5z6jiBfzP2k=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:QFQXZneikI3XBcAxVVfelvu1pvA= In-Reply-To: <vb4rde$22fb4$2@solani.org> Content-Language: en-US Bytes: 1789 On 9/2/2024 10:07 AM, 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. > > Regards, WM > Is this your Dog? https://youtu.be/ADRGgyhX4YE?t=43