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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality --- infinitesimal number system
Date: Wed, 31 Jul 2024 03:19:22 +0200
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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}.