Re: how

Le 03/05/2024 à 13:48, joes a écrit :
By actual infinity I mean what Cantor started but could not stand.
By actual infinity I mean what ZFC claims but cannot maintain.
 It is the idea that infinite sets are fixed such that no element can be added or removed.
It is the idea that the natural numbers reach immediately from 0 until ω such that no number can be inserted between ℕ and ω. If every natural nunmber is increased by 1, then the set is shifted from {1, 2, 3, ...} to {2, 3, 4, ..., ω}.
 Of course the precondition for this theory is that almost all natural numbers are dark, only a tiny initial segment contains numbers that can be applied individually. The increase of every number mentioned above can only be applied collectively.
All natural numbers can be subtracted from the set of all real numbers. ==> They have no successors which must remain.  From all *definable* natnumbers (Peano-natnumbers) however we know that they have ℵo successors. ==> Not all are definable. A huge, infinite subset is dark.
 Regards, WM