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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality --- infinitesimal number system
Date: Tue, 30 Jul 2024 20:30:09 -0500
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On 7/30/2024 8:19 PM, Moebius wrote:
> Am 31.07.2024 um 02:11 schrieb olcott:
>> On 7/30/2024 6:54 PM, Moebius wrote:
>>> Am 31.07.2024 um 01:46 schrieb olcott:
>>>> On 7/30/2024 5:49 PM, Moebius wrote:
>>>>> Am 30.07.2024 um 20:37 schrieb Jim Burns:
>>>>>> On 7/30/2024 1:30 PM, WM wrote:
>>>>>
>>>>>>> [...] between [0, 1] and (0, 1].
>>>>>
>>>>> Could you please explain to me the meaning of the phrase "between 
>>>>> [0, 1] and (0, 1]"?
>>>>
>>>> One can construe them as line segments that differ in length
>>>> by a single geometric point on the number line. I came up
>>>> with that a few years ago with my infinitesimal number system
>>>> that <bla>
>>>
>>> Hint: IR does not comtain any "infinitesimal numbers" (except 0 that 
>>> is).
>>
>> It is the case that the infinite set of points (0, 1] has exactly one 
>> point less than the infinite
>> set of points [0, 1].
> 
> Indeed! The point 0.
> 
> [0, 1] \ (0, 1] = {0}.

Yes. That is the point.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer