Re: how

On 4/15/2024 7:59 AM, WM wrote:

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

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.

Each member of a set
is less or equal to an upper.bound of the set,
because
that is what an upper.bound is.
The least.upper.bound of a set, if it exists,
is an upper.bound of that set (the least),
because
that is what a least.upper.bound is.
If
  [0,n) is different.in.size
  from [0,n+1) and [0,n-1)
then
  [0,n+n) is different.in.size
  from [0,n+n+1) and [0,n+n-1)
Would you (WM) like me to explain that to you?