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

On 1/9/2025 5:16 PM, WM wrote:

On 09.01.2025 21:57, Jim Burns wrote:

On 1/9/2025 3:23 PM, WM wrote:

On 09.01.2025 20:46, Jim Burns wrote:

Do you (WM) disagree with
'finite' meaning
'smaller.than fuller.by.one sets'?

>
That is also true for infinite sets.

>
Apparently it's true for your infiniteᵂᴹ sets.
However,
it's false for our infiniteⁿᵒᵗᐧᵂᴹ sets.

>
It is false for potentially infinite sets.

Thank you.
A lot of what you (WM) object to
is made necessary by that claim.
One of your actuallyᵂᴹ infinite sets requires
an epilogue 𝔻 to a potentiallyᵂᴹ infinite set
in which ∀d ∈ 𝔻: g(d) = d cannot be true.
Which is weird. Very, very weird.
But you (WM) don't mind, as long as it's your own weird.

Whatever claim you (WM) make about infinite sets
is not a claim about _our_ infiniteⁿᵒᵗᐧᵂᴹ sets.

>
I use actual infinity,

¬∀d ∈ 𝔻: g(d) = d

you use potential infinity,

A set larger than each
set smaller.than fuller.by.one sets
is not any of
the sets smaller.than fuller.by.one sets.
It is a set NOT.smaller.than fuller.by.one sets.

best recognizable by the same cardinality of
almost all your sets.

There's a reason that
I spend most of my time here in
the shallow end of the Infinite Pool.
Maybe you can guess what it is.