Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, effectively)

On 1/2/2025 6:35 AM, WM wrote:

On 01.01.2025 01:45, Jim Burns wrote:

On 12/31/2024 1:05 PM, WM wrote:

I don't stop
but know that
every FISON is finite as its name says
and covers at most 1 % of ℕ.
If you don't agree
find a counterexample.

>
No FISON is smaller than 1% of the maximum FISON.

>
{1} is smaller than {101} which is
smaller than all larger FISONs.

...larger FISONs _which exist_
something which frequently goes without saying.
"Larger FISONs which exist" excludes
a maximum FISON.
How we know it's excluded is
NOT
because we can see all FISONs
but
because we can see a description of all FISONs,
and
finite.claim.sequences all true.or.not.first.false,
which must be all true.

Each FISON is a counter.example --
NOT because any of them is larger, but
because no maximum FISON exists, darkᵂᴹ or visibleᵂᴹ.

>
Maximum FISONs cannot be grasped

A description of FISONs can be grasped.
Finitely.many finite.length claims,
each claim of which is true.or.not.first.false
can be grasped.

because they are potentially infinite.

An epilogue 𝔻 to a potentiallyᵂᴹ infinite set A
such that ∀d ∈ 𝔻: g(d) = d
leaves A∪𝔻 also potentiallyᵂᴹ infinite.
No epilogue 𝔻 completesᵂᴹ set A