Re: The non-existence of "dark numbers"

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.
Bob vanishes from {#C:#C<#Cᣕᶜ}ᣕᴮᵒᵇ
which is larger than
  any set C for which there are
  fuller.by.one sets which are larger.
For sets #{0} and smaller,
a swap must end outside to remove Bob.
For sets #{0…1} and smaller,
a swap must end outside to remove Bob.
For sets #{0…2} and smaller,
a swap must end outside to remove Bob.
...
But
{#C:#C<#Cᣕᶜ} is larger than {0}
larger than {0…1}
larger than {0…2}
...
{#C:#C<#Cᣕᶜ} is larger than any set for which
a swap must end outside to remove Bob.
{#C:#C<#Cᣕᶜ} is too large to be any set for which
a swap must end outside to remove Bob.

Our sets do not change.

>
Only if changing isn't changing.

If your sets change,
then your sets are not our sets.
Our sets do not change.
Our sets can represent change by
different, unchanging sets.
Our unchanging sets give us the ability to
_look_ at a finite sequence of claims
and, having seen that
that each claim is true.or.not.first.false,
_know_
with or without understanding the claims,
that each claim is true.
Knowing things is useful.
Our sets do not change.