Re: how

Am 13.06.2024 um 14:22 schrieb Jim Burns:

On 6/12/2024 4:33 PM, WM wrote:

If every number is subtracted,
then no successors remain.
If only definable numbers are subtracted,
then successors remain.

Observation: If "definable numbers" is replaced by "finitely many numbers" WM's nonsense actually seems to make some sense:
| If every number is subtracted,
| then no successors remain.
| If only finitely many numbers are subtracted
| then [infinitely many] successors remain.
Now this one:

ℕ is all natural numbers.
Not more and not less.

*sigh*
| ℕ is THE SET OF all natural numbers
especially in the context of set theory. :-)

for each j ∈ ℕ
there are ℵ₀.many followers in ℕ

Indeed!

Is ℕ more than every j ∈ ℕ?

Huh?!

What is it more?

More nonsense?
| Is ℕ larger than every j in ℕ?
Yeah, if IN is defined due to von Neumann, we actually have that An e IN: n c IN. If we define x < y :<-> x c n and ω := IN, we get the well known theorem: An e IN: n < ω.