Re: Ultimate debunking of Cantor's Theory

On Jul 13, 10:48 am, "Peter Webb" wrote:

I said this last time, I will say it again now.
He is not arguing that you can construct a list
of all Reals in base 2.

I was being sloppy in my desperation, when I suggested
earlier that he was arguing that.

He was correcting somebody who said the Cantor
diagonal proof was easy in base 2,

That would be me.

which it isn't, which is interesting because base 2
is the only base where the Cantor construction can't
be used (in its simplest form).

Yes, that is interesting, and I'm not doubting you.
What I'm still doubting is the original poster's
contrived list.

The problem is that if you just flip bits, you could
end up with a number which is already on the list,

Fine, and I would like to see a demonstration of that,
not that I doubt it in principle.

because (in the example given) the procedure
creates 0.100.. when 0.0111.. is already on the list.

That's where you lose me. Yes, 0.100.. is the same
as 0.0111.. which is already on the *contrived* list.

Now, you only need to show one example where
the Cantor construction fails
to produce a number not on the list, and you can
no longer claim that the number produced by the
Cantor construction is always a number not on the
list. So it is possible it is already on the list.

Yes, I understand that, but I still want to understand
that any such example is valid.

Its easy to get around this problem that (for example)
0.5 = 0.4999... in
other base other than base 2, and if you have a look
at the Cantor construction the problem doesn't exist
in base 10 or any other base (except 2).

The standard workaround in base 2 is to consider pairs
of digits, which is equivalent to using base 4. Not
that this is needed; if the Reals aren't equinumerous
with the integers in base 10, then they aren't in any
base.

I have no problem believing any of that, and again I
clearly understand that 0.0111... is the same as
0.111...

I wont ask you to repeat anything yet again. I'll just
meditate on what looks to me like an obviously bogus
example given by the original poster, which you defend.

I don't know whether the original poster is an idiot
or not, but you obviously are not, and you defend his
example, so I must be missing something. Let me just
think about it for a while, and if the light ever dawns
I will say so.


.

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