A quote from u/Massive-Ad7823 (this community's sole moderator):
>Me: N - is famously infinite.
>Them: But it cannot be actually infinite.
Next time a child tells you that it is possible to keep counting forever, make sure to call them a fool!
Every natural number n has an endsegment {n+1, n+2, n+3, ...}. The first endsegments are
{2, 3, 4, 5, 6, 7, ...}
{3, 4, 5, 6, 7, ...}
{4, 5, 6, 7, ...}
...
Some defenders of set theory claim that the intersection of all endsegments is empty while no endsegment is empty. I call this statement matheology, a touchstone of irrationality.
Regards, WM
N is assumed to be a non-empty ordered set such that the following axioms hold:
(1) Any non-empty subeset of N has a smalles element.
(2) Any element of N with the exception of the smallest has an (immediate) predecessor, which also belongs to N.
(3) N has no largest element.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This axiom system has the nice feature of explicitly "rejecting" the idiotic idea of Mückenheim, that there's a largest element in N.
Source: Hans Rohrbach. Das Axiomensystem von Erhard Schmidt für die Menge der natürlichen Zahlen. Mathematische Nachrichten, vol. 4 (1951), pp. 315–321.