Re: The non-existence of "dark numbers"

On 3/18/2025 5:00 AM, WM wrote:

On 17.03.2025 19:13, Jim Burns wrote:

On 3/17/2025 12:11 PM, WM wrote:

On 17.03.2025 05:23, Jim Burns wrote:

Do you (WM) know what 'finite' means?

>

In mathematics, particularly set theory,
a finite set is
a set that has a finite number of elements.
Informally, a finite set is a set which
one could in principle count
and finish counting.
(Wikipedia)

 From the same page, "Finite Set":
⎛ Any proper subset of a finite set S is finite
⎜ and has fewer elements than S itself.
⎜ ...
⎝ The union of two finite sets is finite,
A set which is finite in Wikipedia's sense
has fuller.by.one sets which are larger and finite
and emptier.by.one sets which are smaller and finite.
'Infinite' is not merely 'big',
not even merely 'darkᵂᴹ and big'.

Therefore,
the set of all finite.sizes does not have
a finite.size.

>
Bob can only disappear in a set of finite size
because all exchanges appear at finite sizes.

Bob disappears from (is swapped from)
each finite set A.
Bob disappears to (is swapped to)
a different finite set A∪{1+max.A},
by ⟨max.A⇄1+max.A⟩
After all the swaps,
without ever disappearing into
anywhere other than a finite set,
Bob disappears out of all finite sets.
The swaps are ⟨n⇄n+1⟩ for all n,
in order by n,
in the emptiest inductive set.

The set of all finite.sizes is same.sized as
the set of all finite sizes and Bob.

>
Give the index where Bob is lost.

Before all the swaps,
Bob is not lost from all finite indices.
After all the swaps,
Bob is lost from all finite indices.
There is no finite index,
either visible or dark,
from which Bob is last.lost,
or to which Bob is last.lost.

Do you agree that
the set of all finite.sizes has
has fuller.by.one sets which are NOT larger
and emptier.by.one sets which are NOT smaller >

>
Stop that gobbledegook.
All exchanges happen at finite sizes.

All exchanges are infinitely.many.

We know what finite site means.

"We"?
You showed you can copy.and.paste.
Did you (WM) read "Finite Sets"?

It is quoted above.

⎛ In mathematics, particularly set theory,
⎜ a finite set is
⎜ a set that has a finite number of elements.
⎜ Informally, a finite set is a set which
⎜ one could in principle count
⎜ and finish counting.
⎜ ...
⎜ Any proper subset of a finite set S is finite
⎜ and has fewer elements than S itself.
⎜ ...
⎜ The union of two finite sets is finite,
⎝
-- Wikipedia, "Finite Set"

Now act accordingly or
confess that you were wrong.

Given all the rhetorical deceits which
you (WM) have chosen to use,
  misleading snips etc.,
you must be aware that
what you are shielding by deceit isn't true.
And yet, here we are,
without your confession of error.
Still.