Re: The non-existence of "dark numbers"

On 16.03.2025 21:08, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

>

No. The definable natural numbers strive to the smallest infinite number
ω. But they are never there.

 Whatever "strive" is supposed to mean.

>
That is supposed to mean what Cantor said. It is potential infinity.
>

N is defined as the smallest
inductive set.

>
>
But that definition is impossible to satisfy. Sets are fixed, inductiove "sets" are variable collections.
>

A proof exists that they are there. ℕ_def contains all numbers the
subtraction of which from ℕ does not result in the empty set.

 That's not a mathematical statement.

>
The numbers 1, 2, 3 are such numbers. They are elements of that set.
>

 It's meaningless gibberish.

>
You clearly know the meaning of these words.

 

Obviously the subtraction of all numbers which cannot empty ℕ cannot
empty ℕ.

 "Empty" in this sense is meaningless.

>
You are not unable to understand the meaning. But you are dishonest.
>

I spent quite a few posts to you
trying to get you to explain what you meant by a number "emptying" a set.
You never gave such an explanation.

>
I informed you several times:
ℕ \ {1, 2, 3, ...} = { }