Re: Does the number of nines increase?

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.

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