Re: More complex numbers than reals?

Am 15.07.2024 um 20:53 schrieb Moebius:

Am 15.07.2024 um 20:31 schrieb Python:

Le 15/07/2024 à 16:46, WM a écrit :

 

Probably the idea was discussed that an inclusion-monotonic sequence of infinite terms could have an empty intersection.

 Which is an extremely trivial state of afairs, Mückenheim.
 Hint: There is no natural number in the intersection of all "endsegments".
 Extremely trivial reason: For each and every n e IN: n !e {n+1, n+2, n+3, ...}. In other words, An e IN: n !e INTERSECTION_(n e IN) {n+1, n+2, n+3, ...}.

Hint: In (classical) mathematics {n+1, n+2, n+3, ...} is an infinite set for all n in IN.
Did you ever meet a "sensible student" who claimed that there is an n in IN such that {n+1, n+2, n+3, ...} is finite?