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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Sat, 29 Jun 2024 20:46:53 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Fri, 28 Jun 2024 18:25:57 +0000 schrieb WM:
> Le 28/06/2024 à 19:23, joes a écrit :
>> Am Fri, 28 Jun 2024 13:55:34 +0000 schrieb WM:
>>> Le 28/06/2024 à 10:38, joes a écrit :
>>>> Am Thu, 27 Jun 2024 12:15:30 +0000 schrieb WM:
>>>>> Le 26/06/2024 à 23:55, Jim Burns a écrit :
>>>>> 
>>>>>> WM thinks an infinite number is very.large.but.finite
>>>>> No, I assume that sets are complete. Therefore ℕ_0 as a proper
>>>>> superset of ℕ has one elements more than ℕ. Infinity does not make
>>>>> them equal.
It does.
> What is immediately before ω?
>> Infinity does not have a predecessor like finite numbers.

>>>> What does „complete” mean?
>>> It means that no natural number can be added to {0, 1, 2, 3, ..., ω}
>> Duh, the set of all natural numbers N contains all of them.
This is misleadingly notated, implying a predecessor. You mean ω u ℕ,
or {ℕ}∪ℕ = {{0, 1, 2, …}, 0, 1, 2, …}. [Neo layout FTW]

>>> It means that the subtraction of the complete set leaves {0, 1, 2, 3,
>>> ..., ω} \ ℕ = {0, ω}.
>>> It means that in {0, 1, 2, 3, ..., ω} before ω there is a natural
>>> number.
>> There is not, since there are infinitely many of them.
> Linearity excludes more than one at a position. Immediately before ω
> there is at most one natural number.
You are confusing the infinitely long, linearly scaled natural number
line with the ordinal number line, which can be drawn with 0, ω, ω*2(?),
ω^2, …(?) at fixed/constant intervals. They do not live in the same
world. You want to shoehorn ω and the rest somewhere onto the infinite
N, continuing in steps of 1. This already fails in finding the non-
existent far end. ω is not connected, as you say, to 0 by a finite
number of steps. It is an augmentation to the whole set, giving a new
anchor. Likewise ω*2 = ω+ω is obviously infinitely far away from ω.


>>>> With which numbers do you describe the sizes of N and N_0?
>>> Most of them are dark and cannot be used as individuals.
>> Not their elements. I was asking for their number, how many of them
>> there are.
> |N| + 1 = |N_0|
And that is…? You gave only a relation.

-- 
Am Fri, 28 Jun 2024 16:52:17 -0500 schrieb olcott:
Objectively I am a genius.