Re: Ultimate debunking of Cantor's Theory

On Jul 17, 8:07 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 16 Jul., 20:45, Virgil <vir...@xxxxxxxxxxx> wrote:



In article <1184602377.255290.254...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 16 Jul., 07:20, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1184550638.931818.34...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
IF one has a non-empty ordered set without a largest element, one can
easily prove

But IF one has an empty non-ordered set with a largest element, what
can one prove then?

How can there be a "largest" if there is no ordering by which to compare
sizes?

Can WM explain how to identify a largest without being able to compare
relative sizes?

Can you explain how you check all lines of an infinite list while
behind every checked line there remain infinitely unchecked lines?

Every line is associated with a natural number n.

If you prove something is true about any line numbered n,
then you have proved it for all lines without having
explicitly checked. Why? Because "any line numbered n"
covers every line. There are no exceptions.

I can declare without checking that all even numbers
end in 0, 2, 4, 6 or 8. In particular, I can declare
with checking that all even numbers of 1000 digits
have that property.

Do you have to check all of the 10^1000/2 1000-digit
numbers to convince yourself of the truth of that
statement?

- Randy

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