Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: Log i = 0 Date: Tue, 27 May 2025 16:50:16 +0200 Organization: A noiseless patient Spider Lines: 22 Message-ID: <1014jf8$2l9jj$3@dont-email.me> References: <100u1hr$164q1$1@dont-email.me> <100v4db$1clol$1@dont-email.me> <100vb6e$1e1uv$1@dont-email.me> <100ve7j$1ek0p$1@dont-email.me> <100vf19$1ela4$1@dont-email.me> <100vfr3$1ek0p$2@dont-email.me> <100vih5$1fh1n$1@dont-email.me> <1011u94$20v84$2@dont-email.me> <1012ioa$25p6h$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 27 May 2025 16:50:17 +0200 (CEST) Injection-Info: dont-email.me; posting-host="477ee35d926c3c7e2ac30469442c5c4f"; logging-data="2795123"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19nr03KR2SyNs6Yj1XQot7tZaDJgTT0iT0=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:HuDbJM14AqDjLLLmv3/XQVwXA4E= Content-Language: en-US In-Reply-To: <1012ioa$25p6h$2@dont-email.me> Bytes: 2086 On 26.05.2025 22:25, efji wrote: > Le 26/05/2025 à 16:36, WM a écrit : >> That is wrong. Present mathematics simply assumes that all natural >> numbers can be used for counting. But that is wrong. > > What's the point ? > It is the DEFINITION of "counting". A countable infinite set IS a set > equipped with a bijection onto \N. > This bijection does not exist because most natural numbers cannot be distinguished as a simple argument shows. All natural numbers can be manipulated collectively, for instance subtracted: ℕ \ {1, 2, 3, ...} = { }. Here all have disappeared. Could all natural numbers be distinguished, then this subtraction could also happen but, caused by the well-order, a last one would disappear. Regards, WM