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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The non-existence of "dark numbers"
Date: Sat, 15 Mar 2025 16:56:12 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 15 Mar 2025 17:49:49 +0100 schrieb WM:
> On 15.03.2025 12:32, joes wrote:
>> Am Sat, 15 Mar 2025 09:56:31 +0100 schrieb WM:
>>> On 15.03.2025 00:11, Alan Mackenzie wrote:
>>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>>
>>>>> ℕ_def contains all numbers the subtraction of which from ℕ does not
>>>>> result in the empty set.
>>>> What does "which" refer to?
>>> It refers to the numbers. An Englishman should comprehend that.
>> It could also have referred to the set. But in this case, N_def=N.
> ℕ_def contains all numbers the subtraction of which from ℕ does not
> result in the empty set.
For every number in N, if you subtract that number, a nonempty set
remains. Of course, if you subtract all of them, nothing does.

> ℕ contains all numbers the subtraction of which from ℕ does result in
> the empty set.
No element of N, subtracted from N, leaves the empty set (because N
contains more than one element).

>>>> To N_def or to a member of the "all numbers"?
>>> That is one and the same.
>> No. N_def is not a number.
> ℕ_def contains all numbers the subtraction of which from ℕ does not
> result in the empty set.
Yes, N_def is a set.
-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.