Re: how

WM schrieb:

Le 14/04/2024 à 22:39, Jim Burns a écrit :

On 4/14/2024 3:12 PM, WM wrote:

Le 13/04/2024 à 21:16, Jim Burns a écrit :

 

if  n < ω
then  2⋅n < ω

>
That is impossible because
doubling is a linear operation.

 
You (WM) have decided that
ω is like all the numbers n < ω

 
Cantor has decided, that ω is an ordinal which can be counted and passed
by counting (Hilbert).

 
Whatever it might mean
to put ω and 1 on the same line,

 
It is Cantor's number classes. See Transfinity p. 42.

 
If n is a number
different.in.size from its nearest.neighbors,
then 2*n is a number
different.in.size from its nearest.neighbors.
 
If n is a number less than
  the least.upper.bound of numbers
  different.in.size from their nearest.neighbors,
then 2*n is a number less than
  the least.upper.bound of numbers
  different.in.size from their nearest.neighbors.

 
That is wrong if all natnumbers are present already such that no further
natnumbers fits below ω.

With Dedekind, all infinite sets like IN are having proper subsets and have
therefore real supersets so there is any required "place" in infinite sets.
 

If  n < ω
then  2*n < ω

If  n < ω
then  n^n < ω

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