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Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> Newsgroups: sci.math Subject: Re: Does the number of nines increase? Date: Fri, 28 Jun 2024 20:04:38 -0700 Organization: A noiseless patient Spider Lines: 70 Message-ID: <v5ntk7$3o6f3$2@dont-email.me> References: <tJf9P9dALSN4l2XH5vdqPbXSA7o@jntp> <9f744198-219c-481d-970d-0ba4c264f090@att.net> <4RWgJcGMg1Zagk6yT04mcwxdZH4@jntp> <v5hnm4$29b21$1@dont-email.me> <sfW0pg19oa0A7b2GJjbP8AlAwb0@jntp> <v5kg4u$2spnv$1@dont-email.me> <Q9Ty9BfiECefxiGIeT9CRf3Uf3s@jntp> <v5khhr$2t9ge$1@dont-email.me> <n8yFCTYzvxeMHg_Y_lLeGwaOCQk@jntp> <v5mrau$1d3t3$6@i2pn2.org> <cFS6RtUWz5LZnEWG2b4uQjn32bQ@jntp> <v5nd8f$3hovk$2@dont-email.me> <OZWcnZx5r_EVwOL7nZ2dnZfqn_idnZ2d@giganews.com> <v5nq68$3nq5r$1@dont-email.me> <ss2cnR7ruKJe6eL7nZ2dnZfqn_adnZ2d@giganews.com> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 29 Jun 2024 05:04:39 +0200 (CEST) Injection-Info: dont-email.me; posting-host="1dec0191834013eb7d293450cfe2cb7e"; logging-data="3938787"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX187WX+22bSOPouQQJGHiiHMHP3xocDajhY=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:gSQWt7CGNUsB+7Bl2cH+S0bv3cA= Content-Language: en-US In-Reply-To: <ss2cnR7ruKJe6eL7nZ2dnZfqn_adnZ2d@giganews.com> Bytes: 3364 On 6/28/2024 7:43 PM, Ross Finlayson wrote: > On 06/28/2024 07:05 PM, Chris M. Thomasson wrote: >> On 6/28/2024 6:04 PM, Ross Finlayson wrote: >>> On 06/28/2024 03:25 PM, Chris M. Thomasson wrote: >>>> On 6/28/2024 11:21 AM, WM wrote: >>>>> Le 28/06/2024 à 19:19, joes a écrit : >>>>>> Am Fri, 28 Jun 2024 13:59:02 +0000 schrieb WM: >>>>>>> Le 27/06/2024 à 22:20, "Chris M. Thomasson" a écrit : >>>>>>> >>>>>>>> There is always an infinite number of nines in Say: >>>>>>>> 9.(9) = 10 >>>>>>>> >>>>>>> Is in 9.999... one 9 more than in 0.999... when 9.999... has been >>>>>>> produced by multiplying 0.999... by 10? >>>>>>> Is in 9.999... one 9 more than in 0.999... when 9.999... has been >>>>>>> produced by adding 9 to 0.999...? >>>>>> No, they both have infinitely many 9s. It does not matter how they >>>>>> were „produced”. >>>>> >>>>> Then the set of indices is not constant. Try again. >>>>> >>>>>> They are the same number 10. >>>>> >>>>> Wrong. Try again. >>>> >>>> Did you get dropped on your head at a really young age or something? >>>> >>>> ;^o >>>> >>> >>> How many times do you multiply it by ten? You know, add a zero? >>> >>> >> >> (.999...) * (9.999...) = (9.999...) >> >> (9.999...) * 10 = (99.999...) >> >> (99.999...) * 10 = (999.999...) >> >> Where are the missing nines? ;^) > > Oh, so you add 9's, .... > > r[0] = .9 r[n] = r[n] + 10^(-n) * .9 Should show infinite nines .999... wrt a summation. // expand: r[0] = .9 r[1] = .9 + 10^(-1) * .9 = .99 r[2] = .99 + 10^(-2) * .9 = .999 .... Heck, even r[0] can be: .0 + 10^(-0) * .9 So: r[0] = .0 + 10^(-0) * .9 = .9 r[1] = .9 + 10^(-1) * .9 = .99 r[2] = .99 + 10^(-2) * .9 = .999 r[3] = .999 + 10^(-3) * .9 = .9999 .... :^)