Re: Replacement of Cardinality --- infinitesimal number system

Am 31.07.2024 um 03:30 schrieb olcott:

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].

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Indeed! The point 0.
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[0, 1] \ (0, 1] = {0}.

 Yes. That is the point.

Remember that I originally wrote:
"Could you please explain to me the meaning of the phrase "between [0, 1] and (0, 1]"? What IS "between [0, 1] and (0, 1]". (Which real numbers are "between [0, 1] and (0, 1]"? 0? So why not just talk about 0 in this case?)"
Thank you for your contribution. EOD.