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

Jim Burns schrieb:

On 4/26/2024 10:37 AM, WM wrote:

Le 26/04/2024 à 01:11, Jim Burns a écrit :

On 4/25/2024 4:03 PM, WM wrote:

 

If all smaller numbers are doubled,
then there is no place for
the doubled numbers below ω.

>
If n is below ω
then n can be counted to from 0
then n⋅2 can be counted to from n

>
That is true for definable numbers
but not for the last numbers before ω.

 
If any number below n canNOT be counted to from 0
then n itself canNOT be counted to from 0
 
Thus,
each number which CAN be counted to from 0
is not above
any number which canNOT be counted to from 0
 
By definition,
ω is between
numbers which CAN be counted to from 0 and
numbers which canNOT be counted to from 0
 
Imagine being someone who denies that definition of ω
 
Because the following isn't a claim about ω
you (the denier) should still admit:
if n can be counted to from 0
then n*2 can be counted to from n
then n*2 can be counted to from 0 (through n)
 
If ω exists as defined,
then doubling never crosses ω
(from CAN to canNOT)
 
Even if ω doesn't exist as defined,
then doubling never crosses
_where ω would be if ω existed_
(from CAN to canNOT)
 
 
ω is NOT a simply.humongous.instance of
the numbers 0 1 2 3 ...
ω marks a boundary between domains with
different descriptions (CAN and canNOT).
 
Imagine being someone who denies that
ω marks that boundary.
With or without the marker,
the domains (CAN and canNOT) remain
the domains (CAN and canNOT).

This is really well put!

Unfortunately, WM is not interested in our ideas of (our) math and
logic but in his own (mostly read up upon) ideas and his flexible
and willingly deformable "true logic" which a "normal" person can
even "feel" -- but even more is WM interested in (we) WHAT folks
CLAIM and STATE about (our) math, more than about that math itself.