Re: how

On 6/18/2024 4:09 PM, WM wrote:

Le 18/06/2024 à 19:12, Jim Burns a écrit :

If all numbers having ℵ₀ followers are removed
then no numbers remain.

>
Note that the ℵ₀ followers are not removed.

Followers having ℵ₀ followers are removed.
There aren't any other not.removed followers.

There is no first number remaining.

>
Correct.
>

There is no number remaining.

>
Wrong.

For subsets of the minimal inductive meta.set
{i:∀₃Xᴬ⤾⁺¹₀:X∋i}
only the empty set does not hold a first element.
If the set of numbers.remaining
  does not hold a first element,
then the set of numbers.remaining
  is the empty set.

We can _define_ a number that remains;

>
No.

Yes.
That is less important than you think it is.
The definiens states what the definiendum means
_to the definer_
In regard to _what the definer means_
that statement receives a presumption of truth.
We presume the definer is aware of what they think
and that they're being honest about that.
We can define _flying rainbow sparkle pony_
to mean a number that remains.
And it is thereby defined.
Does a flying rainbow sparkle pony _exist_ ?
If it does exist, _it's not by definition_
Defining things _to exist_ is silly.
A FRSP exists or doesn't exist.
If an FRSP exists, hooray, it satisfies
that part of its definition.
If a FRSP _doesn't_ exist, then
everything is true of a non.existing thing:
it doesn't exist, it exists, it flies,
it doesn't fly, whatever.
So, not.existing.FRSP _still_ satisfies
its definition. And doesn't exist.
Defining a FRSP to exist says nothing
about it existing or not.
It's the same lame trick as defining God as
a being with all good properties, and defining
existence as a good property. It would be bizaare
if God could be poofed into existence like that.
It would be as bizarre for darkᵂᴹ numbers.

however,
the _existence_ of the number defined
leads to self.contradiction

>
Therefor you cannot define a number that remains.

I can define a number that remains and  then
prove it doesn't exist.