On 29 Mrz., 22:56, Virgil <Vir...@xxxxxxxxx> wrote:

It is an artifact of the completion of any infinite process that
something exists that did not exist at any stage of the process.
The something, in this case, includes all those uncountably many
unconstructed paths.

But if we

accept it, then we must accept this also for Cantor's list. The
following list

0.0
0.1
0.11
0.111
...,

after completing construction, also contains the path 0.111....

A list is not a tree, and a listing does not ever list any object whose
position in the list does not exist.

Neither does a tree contain any path that was not used for
construction (in my proof A).

Then however, the diagonal number 0.111... that you construct in above
list, when replacing 0 by 1, is in the list.

Not as a member of any mathematically acceptable list.

So paths can creep, as sequences of bits, into lists but cannot creep,
as sequences of digits, into lists. How lucky we are that paths know
the difference!.

So that WM claims that there are finite sets of naturals numbers that DO
NOT have largest members?

In what freak show can one find such wonders displayed?

In reality.

Regards, WM
.

• References:

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