Re: how

On 6/14/2024 4:34 AM, WM wrote:

Le 13/06/2024 à 20:25, Jim Burns a écrit :

On 6/13/2024 10:55 AM, WM wrote:

Every number has ℵo successors.

Yes.

If every number which hasn't ℵ₀ successors
is deleted,
then none are deleted.
>

If every number is subtracted
the successors remain.

>
If every number which has ℵ₀ successors
is deleted,
then none remain.

>
Try to think better.
The successors are not deleted.

You:

Every number has ℵo successors.

Every number which has ℵ₀ successors is
every number.
If every number
is deleted,
then none remain.

Explanations should be as simple as possible,
but no simpler.

>
Here is the simplest possible explanation:

No, simpler than possible.

If all numbers which have ℵo successors
are deleted from ℕ,

...and

Every number has ℵo successors.

then ℵo successors remain in ℕ

...then successors which haven't ℵ₀ successors
remain in the new not.ℕ set.
That is 0 successors.

- in every step

Any step other than a step such that
⎛ all numbers which have ℵo successors
⎝ are deleted from ℕ
is an irrelevant step.

and, if existing, in the limit.
But every definable number is deleted.
None remains.

You:

Every number has ℵo successors.