Re: Incompleteness of Cantor's enumeration of the rational numbers

On 11/27/2024 04:32 AM, Richard Damon wrote:

On 11/27/24 5:12 AM, WM wrote:

On 26.11.2024 18:50, Richard Damon wrote:

On 11/26/24 11:59 AM, WM wrote:

On 26.11.2024 16:06, Richard Damon wrote:

On 11/26/24 6:24 AM, WM wrote:

On 26.11.2024 12:15, FromTheRafters wrote:

WM pretended :

>

It is impossible to change |ℕ| by 1 or more.

>
Right, sets don't change. The set {2,3,4,...} does not equal the
set of natural numbers, but |{2,3,4,...}| does equal |N|.
>

Then your |N| is an imprecise measure. My |N| is precise.
|{2,3,4,...}| = |N| - 1 =/= |N| .

>

Then your measure is incorrect, as by the DEFINITION of measures of
infinite sets, all countably infinite sets have the same "measure".

>
That is one special definition of a very imprecise measure. We can
do better.

>
But maybe you can't and get something consistant.

>
Of course. |{1, 2, 3, 4, ...}| = |ℕ| and |{2, 3, 4, ...}| = |ℕ| - 1 is
consistent.
>
Regards, WM
>
>

>
So you think, but that is because you brain has been exploded by the
contradiction.
>
We can get to your second set two ways, and the set itself can't know
which.
>
We could have built the set by the operation of removing 1 like your
math implies, or we can get to it by the operation of increasing each
element by its successor, which must have the same number of elements,
so we prove that in your logic |ℕ| - 1 == |ℕ|, which is one of Cantor's
claim, and what you want to refute, but comes out of your "logic"
>
So saying that |ℕ| -1 is different than |ℕ| just makes your logic
inconsistant.

Tossing WM's failures in definition into your mathematician's waste-bin,
doesn't fix that his other failures of definition
reflect things that _are_ mathematical objects, that the usual
sort of notion is "don't toss the baby with the bath-water",
that after washing the baby is involved tossing the dirtied water
yet not the baby itself, that behind the screeching howler troll
bot, is another student, and this one wants explanations about
how the pair-wise switching of units, and pushing out those
accessed or indexed "to infinity", that the second student
_does_ have a contradiction from following his definitions,
that now your straw-man soft-ball pinata (pinyata) has
resulted the spoils beneath not palatable, and the one he
wants you've stuck in the tree.