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

On 5/6/2024 2:59 PM, WM wrote:

Le 05/05/2024 à 19:59, Jim Burns a écrit :

On 5/3/2024 4:31 PM, WM wrote:

If all could be counted to,
they would not remain after every counted number.

Of those which CAN be counted.to,
each CAN be counted to.

From each number n which CAN be counted.to
for each number k which CAN be counted.to
more.than.k numbers which CAN be counted.to
can be reached immediately
from n to n+k+1
>
None of these immediate more.than.k numbers remain
after every number n which CAN be counted.to.

>
Nevertheless almost all, namely ℵo, remain.

Of those which CAN be counted.to,
each CAN be counted to,
and
none remain after all which CAN be counted.to,  and
each has its own immediate followers  such that
  each follower
    CAN be counted.to  and
    does NOT remain after all which CAN be counted.to
  and
  they are more.than.1.many
    "Infinite" does not mean "humongous".
Of those which CAN be counted.to,
each CAN be counted to,
and
none remain after all which CAN be counted.to,  and
each has its own immediate followers  such that
  each follower
    CAN be counted.to  and
    does NOT remain after all which CAN be counted.to
  and
  they are more.than.2.many
Of those which CAN be counted.to,
each CAN be counted to,
and
none remain after all which CAN be counted.to,  and
each has its own immediate followers  such that
  each follower
    CAN be counted.to  and
    does NOT remain after all which CAN be counted.to
  and
  they are more.than.3.many
...
Of those which CAN be counted.to,
each CAN be counted to,
and
none remain after all which CAN be counted.to,  and
each has its own immediate followers  such that
  each follower
    CAN be counted.to  and
    does NOT remain after all which CAN be counted.to
  and
  they are more.than.k.many
...
Of those which CAN be counted.to,
each CAN be counted to,
and
none remain after all which CAN be counted.to,  and
each has its own immediate followers  such that
  each follower
    CAN be counted.to  and
    does NOT remain after all which CAN be counted.to
  and
  they are more.than.any.countable.to
  they are ℵ₀.many