Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Thu, 5 Dec 2024 20:25:34 +0100 Organization: A noiseless patient Spider Lines: 24 Message-ID: References: <87frn50zjp.fsf@bsb.me.uk> <87y10vzo35.fsf@bsb.me.uk> <87ser3zgez.fsf@bsb.me.uk> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 05 Dec 2024 20:25:34 +0100 (CET) Injection-Info: dont-email.me; posting-host="e460a63d8fc463190e759e7a758b0cfb"; logging-data="1893447"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+J4GLKwQpvAxDLugQ/wOkTr+YGRUYCH7M=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:ReAElpLqroUSUsceNeGaUu/+Zpw= In-Reply-To: Content-Language: en-US Bytes: 2642 On 05.12.2024 17:50, FromTheRafters wrote: > WM pretended : >> On 05.12.2024 14:40, FromTheRafters wrote: >>> WM used his keyboard to write : >> >>>> All means all with no exception. But every number you can take >>>> belongs to a vanishing subset of ℕ. >>> >>> What do you mean by vanishing? >> >> The subset of numbers that can be taken is ℕ_def. It is smaller than >> |ℕ|/k for every k ∈ ℕ. >> >> Have you meanwhile found an example for sequences with terms a_n = b_n >> for every n but different limit? > > Why should I? Your answer to Identical sequences have the same limit: "Running with buffaloes does not make one a buffalo" appeared to doubt my claim. Regards, WM