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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality (infinite middle)
Date: Sun, 11 Aug 2024 22:21:28 +0200
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Am 11.08.2024 um 21:29 schrieb Chris M. Thomasson:
> On 8/11/2024 9:10 AM, Moebius wrote:
>> Am 11.08.2024 um 06:20 schrieb Chris M. Thomasson:
>>> On 8/10/2024 6:19 PM, Moebius wrote:
>>>> Am 11.08.2024 um 02:55 schrieb Chris M. Thomasson:
>>>>> On 8/10/2024 4:05 PM, Moebius wrote:
>>>>
>>>>>> I guess, JB would say: "If we don't consider omega, we don't 
>>>>>> consider omega." :-P
>>>>>
>>>>> For some reason I am thinking of salad here...? ;^)
>>>>
>>>> You won't agree? :-)
>>>
>>> I can see a line, comprised of two n-ary points. They have a p0 and a 
>>> p1, yet there is an infinity between then. [etc. etc.]
>>
>> And where do you see omega on that line? (Very ... VERY ... far away?)
>>
>> https://www.youtube.com/watch?v=jvQ6dasK614
> 
> I guess its basically "out of scope" in a sense?

Yeah, but "just not there" might be more appropriate.

You see: "If we don't consider omega, we don't consider omega."

Let me try to explain. If we consider the interval [0, 1] of real numbers:

|-----------------|
0                 1

then 2 is not on this line segment: it's just not there. :-)

But the case with omega is worse:

It's not on the real line at all. omega !e IR.

On the other hand we *may* extend the "real number line".

See: https://en.wikipedia.org/wiki/Extended_real_number_line