Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

On 5/3/24 9:57 AM, WM wrote:

Le 03/05/2024 à 11:07, Jim Burns a écrit :
 

WM call various things
"actually infinite" and "potentially.infinite".
What does he mean by those terms?
NOT "What does Cantor mean? Euclid mean?"

 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}.

Which just means you don't understand the nature of "unbounded" sets.
(like Sets where there does not exist an upper bound for the set in the set itself).
Of course, part of the problem is you are trying to use logic that restricts itself to finite sets, and thus can't actually handle the things you want to try to handle with it.

 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.

Which is a statment that you can not maintain, as there is no upper limit to the numbers that can be applied individually.
Yes, we can only talk about an infinite subset of numbers collectively, but every Natural Number is also a member of finite sets where it CAN be used individually.
Some operations can only be done collectively (or only done collectively on some subsets).

 Regards, WM