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Subject: Re: Replacement of Cardinality --- infinitesimal number system
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Tue, 30 Jul 2024 18:55:29 -0700
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On 07/30/2024 05:22 PM, FromTheRafters wrote:
> olcott presented the following explanation :
>> 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.
>
> An accumulation point. How big is it? How big must it be to affect length?

https://www.youtube.com/watch?v=HsGOZp7jrEY&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=6

"Non-standard analysis:  continuum infinitesimal analysis, and sweep"