Re: Cantor Confusion

On Fri, 05 Jan 2007 10:37:01 EST, Andy Smith wrote:
But anyway, what integer does your mapping map 1/3 (a real in [0,1])
to?

It would map to ..0101010 !

That's not an integer

It is the natural successor to ..0101001 !

That's not an integer either.

But I agree it is hard to see how one can count up to
..0101010 from 0. As I said in my earlier post, I am
suspicious of anything to do with infinite sets. But what
is wrong with my systematic technique for counting the
reals, and how does it differ substantively from mapping
the rationals onto the natural numbers?

I thought that was already answered. If your method >actually works, then
it should map some integer to 1/3. Which one is it?

I should say that I am not sufficently barking to think
that Cantor is wrong, just trying to get my head
straight, and informed advice is welcome ...

My advice is, once an error in your reasoning has been pointed out, don't
simply ignore it and continue asking where the error is.


Thank you for your (disdainful) advice. However, you didn't point out
where the error was, you just baldly stated that ..0101010 was
not an integer. You can count up to ..0101010 in a (countably) infinite number of steps M by the iteration:

N0 = 2
{
Nm = N(m-1)+ N(m-1)+2
}

Do the first iteration in 1 second, the second in 1/2 second,
third in 1/4 second etc. and in precisely 2 seconds you will have generated
..0101010

Like I said, I am suspicious of arguments involving infinite sets.
.

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