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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!news.nobody.at!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Moebius Newsgroups: sci.math Subject: Re: Does the number of nines increase? Date: Tue, 16 Jul 2024 03:39:26 +0200 Organization: A noiseless patient Spider Lines: 33 Message-ID: References: <53214031-3ad1-48bd-8584-0720ec5b28dd@att.net> <79JoZp5bHCH4hf4J9cxbLGeMvPE@jntp> <74edd85cf4bdd0aecaee742ef35763e9d9dc8741@i2pn2.org> Reply-To: invalid@example.invalid MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 16 Jul 2024 03:39:26 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f7b47e05a7b4f9518fb2a2693f1d498d"; logging-data="1005070"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19931+06AHstreZhzciB2CO" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:YiM/WCDeIZ82JZo6CRXW2GLb810= In-Reply-To: Content-Language: de-DE Bytes: 2357 Am 16.07.2024 um 03:27 schrieb Chris M. Thomasson: > Naturals: > > a = any natural number > b = a + 1 is the /successor/ of a? > > ;^) Hell, man, you are asking questions... :-) Ok, starting with the Peano-axioms there is a functions called /the successor function/ s. Then THE successor of, say, n is s(n). :-) Based on the Peano-axioms we usually define "addition" + ("recursively") the following way: n + 0 = n n + s(m) = s(n + m). Moreover we (usually) have the definition: 1 := s(0). "1 is the successor of 0". Hence n + 1 = n + s(0) = s(n + 0) = s(n). So, yes, a + 1 is indeed the successor of a (for any a e IN).