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From: Richard Damon <richard@damon-family.org>
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)
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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 <Keith.S.Thompson+u@gmail.com> writes:
>>>
>>>> olcott <polcott333@gmail.com> writes:
>>>>> On 4/3/2024 12:23 PM, Keith Thompson wrote:
>>>>>> "Fred. Zwarts" <F.Zwarts@HetNet.nl> 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.