Re: The non-existence of "dark numbers"

On 3/21/2025 2:15 PM, WM wrote:

On 21.03.2025 18:39, Jim Burns wrote:

On 3/21/2025 3:50 AM, WM wrote:

On 20.03.2025 23:25, Jim Burns wrote:

For sets not.having a WM.size,
Bob vanishing isn't a size.change.

>
Only if reducing isn't reducing.

>
What you (WM) think is reducing
isn't reducing.

>
You confuse
the clear fact that
in the reality of
sets vanishing means reducing
with
the foolish claim that
cardinality was a meaningful notion.

The set of all sizes.which.WM.considers.sizes
does not have a size.which.WM.considers.a.size.
You (WM) have rules for
sets with sizes.which.WM.considers.sizes
rules which aren't intended for
sets without sizes.which.WM.considers.sizes
Your rules aren't intended for
the set of all sizes.which.WM.considers.sizes.

Learn that
even Cantor has accepted that
the positive numbers have more reality than
the even positive numbers.

Without context, I can't be sure, but
I suspect that
Cantor's "more reality" and
Zermelo's "simplest" serve
the same purpose as my "emptier" and "fuller",
which is to rank infinite sets by
something _other than_ by size.
This gives us the vocabulary to discuss
the difference between finite and infinite sets:
In all and only infinite sets,
reality, simplicity, emptiness and fullness
can change while, at the same tine,
size stays the same.
In finite sets, otherwise.

He said that is not in conflict with
the identical cardinality of both sets.

Thank you.
Two sets of the same cardinality,
one a proper subset of the other,
can be swapped set.wise, one for the other,
and preserve size.
Either swapping all at once,
or swapping in infinitely.many singleton.swaps,
size is preserved,
but reality;simplicity;fullness isn't preserved,
and Bob can disappear without leaving.

And he was right!
"Counable" is simply
another name for potential infinity.

A set larger than
any set from which Bob cannot disappear
is not
any set from which Bob cannot disappear.

Therefore
vanishing odd numbers means
reducing the reality of the set.

The odd naturals are a proper.subset of
odd and even naturals, even though
they have the same cardinality.
In other news,
f(k) = 2k+1 disappears the evens.
Perhaps these facts are related, somehow.
What do you think?

Therefore the sentence
"What you (WM) think is reducing isn't reducing" exhibits you as a snooty dilettante who
cannot distinguish between cardinality and reality.

If
you (WM) now distinguish between cardinality
and reality;simplicity;fullness,
then
you have grasped what I have been telling you
for years.
Literally. Years.
(It's possible I'm jumping the gun here.)
As for my inability to distinguish cardinality
from reality;simplicity;fullness:
why, yes, of course,
we have always been at war with Eastasia.