Path: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: joes Newsgroups: sci.math Subject: Re: The non-existence of "dark numbers" Date: Sat, 15 Mar 2025 11:26:14 -0000 (UTC) Organization: i2pn2 (i2pn.org) Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Injection-Date: Sat, 15 Mar 2025 11:26:14 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="277972"; mail-complaints-to="usenet@i2pn2.org"; posting-account="nS1KMHaUuWOnF/ukOJzx6Ssd8y16q9UPs1GZ+I3D0CM"; User-Agent: Pan/0.145 (Duplicitous mercenary valetism; d7e168a git.gnome.org/pan2) X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 3153 Lines: 42 Am Fri, 14 Mar 2025 23:10:11 +0100 schrieb WM: > On 14.03.2025 16:21, Alan Mackenzie wrote: >> WM wrote: > >>> Perhaps everybody is unable to see that ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, >>> ..., n}| = ℵo? >> Everybody can see that, and everybody but you can see it has nothing to >> do with the point it purportedly answers. > ℕ_def contains all numbers the subtraction of which from ℕ does not > result in the empty set. This makes NO SENSE. You either mean N_def=N (no single removed number makes the set empty *facepalm*) or N_def={} (subtracting everything makes the set empty). > Obviously the subtraction of all numbers which > cannot empty ℕ cannot empty ℕ. What? Is N_def finite? (don't come at me with "potential"). >> Wrong. It is an "instantaneous" definition which completes N. > Yes, of course. But ℕ_def is not completed by its definition. wat >> There are >> not various stages of "N" which are in varying stages of completion. > ℕ_def is never complete. Then it is not a set. If it were, it would equal N. >>> There is place to strive or tend. >> The tending takes place, but not in a "place". > No? Tending means that hitherto undefined natural numbers become > defined. That takes place on the ordinal line. No. What's undefined doesn't exist. "Tending" is a property of a sequence, not of individual numbers. >> That I have to write such nonsense to answer your point shows the great >> deterioration which has taken place in a once vital newsgroup. > Hardly to believe that matheology like tending of ordinals outside of > the ordinal line has ever been useful. You got that wrong. -- 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.