Path: ...!news.misty.com!weretis.net!feeder6.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: comp.theory Subject: =?UTF-8?Q?Re=3A_Definition_of_real_number_=E2=84=9D_--infinitesimal?= =?UTF-8?Q?--?= Date: Thu, 4 Apr 2024 08:09:58 -0400 Organization: i2pn2 (i2pn.org) Message-ID: References: <87h6gijr6l.fsf@nosuchdomain.example.com> <878r1ujjhs.fsf@nosuchdomain.example.com> <87il0yt7rq.fsf@bsb.me.uk> <7OqdnXRmmZCikZP7nZ2dnZfqn_idnZ2d@giganews.com> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 4 Apr 2024 12:09:58 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="55746"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird Content-Language: en-US In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 4918 Lines: 71 On 4/3/24 10:35 PM, olcott wrote: > On 4/3/2024 9:11 PM, Ross Finlayson wrote: >> On 04/03/2024 03:12 PM, Ben Bacarisse wrote: >>> Keith Thompson writes: >>> >>>> olcott writes: >>>>> On 4/3/2024 12:23 PM, Keith Thompson wrote: >>>>>> "Fred. Zwarts" writes: >>>>>> [...] >>>>>>> Olcott is unable to understand  what it says in the context of the >>>>>>> real number system, even when spelled out to him in great >>>>>>> detail. Therefore he sticks to his own (wrong) interpretation and >>>>>>> then >>>>>>> starts to fight it. Fighting windmills. >>>>>> Might I suggest waiting to reply to olcott until he says something >>>>>> *new*.  It could save a lot of time and effort. >>>>> >>>>> 0.999... everyone knows that this means infinitely repeating digits >>>>> that never reach 1.0 and lies about it. I am not going to start lying >>>>> about it. >>>> >>>> (I don't read everything olcott writes, but that *might* be something >>>> new.) >>>> >>>> Nobody here is lying.  (I'm giving you the benefit of the doubt.) >>>> Some people here are wrong. >>>> >>>> You might take a moment to think about *why* so many people would be >>>> motivated to lie about something like this.  Is it really plausible >>>> that multiple people (a) know in their hearts that you're right, >>>> but (b) deliberately pretend that you're wrong? >>> >>> PO is in a genuine bind here.  He has almost no ability to understand >>> other people's mental states, let alone their reasoning.  He can't begin >>> to comprehend what others think, and he struggles to understand what >>> they write, so he often thinks that people are lying or playing head >>> games.  He's accused me of this numerous times, and (the final straw for >>> me) that I must be doing this deliberately and sadistically.  What other >>> conclusion can he come to? >>> >>> Every time PO paraphrases someone's reply to him he gets it wrong.  He >>> simply does not know what people are saying but since they disagree with >>> something that is obvious to him, they must be stupid, lying or playing >>> head games. >>> >>> The classic technique in mediation where each person must reflect back >>> to the other what it is they believe the other is saying would, were he >>> capable of it, be useful here.  But he would fail at every step. >>> >> >> >> About the di-aletheic, .... >> >> https://www.youtube.com/watch?v=vbyFehrthIQ&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=23&t=1305 >> >> About statements and fact and retraction, .... >> >> https://www.youtube.com/watch?v=tODnCZvVtLg&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=15 >> >> >> Iota-values:  the word "iota" means "smallest non-zero value". >> >> Real-values:  all the values between negative infinity and infinity. > > So the geometric point immediately adjacent to 0.0 on the positive > side of the number line would be a real number. > A Point "Immediately adjacent" doesn't exist. The problem is that points, like Real Numbers, are "dense" and between ANY two of them, are an infinite number of other points.