Re: Replacement of Cardinality --- infinitesimal number system

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].