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Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters <FTR@nomail.afraid.org> Newsgroups: sci.math Subject: Re: Does the number of nines increase? Date: Wed, 26 Jun 2024 06:36:54 -0400 Organization: Peripheral Visions Lines: 39 Message-ID: <v5gr0b$23jb0$1@dont-email.me> References: <tJf9P9dALSN4l2XH5vdqPbXSA7o@jntp> <v5fj5p$1p64h$1@dont-email.me> <PmOdnePzO5XW_Ob7nZ2dnZfqn_WdnZ2d@giganews.com> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-15"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 26 Jun 2024 12:36:59 +0200 (CEST) Injection-Info: dont-email.me; posting-host="779a3826632ddbab160f570284a648b7"; logging-data="2215264"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19zlyhQ0AV+S/0q+BcJLLmM/mg0aSN1uo4=" Cancel-Lock: sha1:1hx8O+KFZfOpL2n4IumLyuwxnHI= X-Newsreader: MesNews/1.08.06.00-gb X-ICQ: 1701145376 Bytes: 2437 Ross Finlayson has brought this to us : > On 06/25/2024 04:17 PM, FromTheRafters wrote: >> WM used his keyboard to write : >>> Let the infinite sequence 0.999... be multiplied by 10. Does the >>> number of nines grow? >> >> No, both sequences are infinite. >> >>> Corollary-question: Does the number of nines grow when in 0.999 the >>> decimal point is shifted by one or more position? >> >> What do you think multiplying by ten does to a continued decimal >> expansion representation? > > What does Simon Stevin say? > > The number of nines left of the radix grows, .... > > Though, one might aver it's the "count" of nines, > it's also its number. > > Counting and numbering are two different things, > though they're often conflated, not to be confused. > > Numbers "have" a number and "make" a count. ....000099.999... There are countably many nines on either side of the radix point. This is a 'representation' of a number which has a countably infinite sequence of symbols left *and* right of the radix. Left of the radix point it has countably infinitely many zeroes and finitely many non-zero symbols. Right of the radix it has countably infinitely many symbols which in this case is all nines and possibly finitely many non-zero and non-nine leading symbols. ....000100.000... Same number but no nines.