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: Sun, 27 Oct 2024 12:54:38 -0700 Organization: A noiseless patient Spider Lines: 29 Message-ID: References: <5e5ccee7-0c98-4701-aeaa-4950a3ce2938@att.net> <08a00c75-bf8d-4f9c-816a-83b8517ca04e@att.net> <062a0fa5-9a15-4649-8095-22c877af5ebf@att.net> <276fc9df-619b-4a10-b414-a04a74aa7378@att.net> <88e6a631-417a-4dd0-9443-a57116dcbd28@att.net> <7a1e34df-ffee-4d30-ae8c-2af5bcb1d932@att.net> <6a90a2e2-a4fa-4a8d-83e9-2e451fa8dd51@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sun, 27 Oct 2024 20:54:39 +0100 (CET) Injection-Info: dont-email.me; posting-host="9f277b258384b51a19551de63f05f922"; logging-data="612004"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/1+66APpTKkkG2g/Xur4XOR7rJW05XXbE=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:UyKqs2SqBWDMqj1Ka2rmNqVyKik= In-Reply-To: Content-Language: en-US Bytes: 3088 On 10/27/2024 4:38 AM, Richard Damon wrote: > On 10/27/24 3:38 AM, WM wrote: >> Am 26.10.2024 um 21:35 schrieb Chris M. Thomasson: >>> On 10/26/2024 9:04 AM, WM wrote: >>>> On 26.10.2024 05:21, Jim Burns wrote: >>>>> On 10/25/2024 3:15 PM, WM wrote: >>>> >>>>>> Mainly, among other points, the claim that >>>>>> all unit fractions can be defined and the claim that >>>>>> a Bob can disappear in lossless exchanges. >>>>> >>>>> The proof that all unit fractions can be defined >>>>> is to define them >>>>> as reciprocals of positive countable.to.from.0 numbers. >>>>> >>>>> That describes all of them and only them. >>>> >>>> No, you falsely assume that all natnumbers can be defined. >>> >>> Huh? Confusing to me. Humm... Are you trying to suggest that a >>> natural number can _not_ be a natural number? >> >> No. But most natnumbers cannot be defined. This can best be understood >> by the unit fractions. > > So, what is the line between the DEFINED natural numbers and the "not > defined"? The dark radii? Just guessing... ;^)