Re: Cantor Confusion


David Marcus schrieb:

mueckenh@xxxxxxxxxxxxxxxxx wrote:
David Marcus schrieb:
You wrote that "A covers B" means that A has at least as many bars as B.

Does "S is completely covered by at least one element of the infinite
set of finite unary numbers" mean that S is covered by an A that has a
finite number of bars?

If S = 0.111... had only finite positions then it was covered by finite
numbers. All of them are in the list (these are unary representations
of the natural numbers)
1 = 0.1
2 = 0.11
3 = 0.111
...
If a set of finite numbers of the list cover some number x of the list,
then always already one list number is sufficient to cover number x. If
some number y (in unary representation) is not in the list, then it
cannot be covered by any list number. Then its positions are not well
defined. This is the case with S.

Sorry, but I don't know what you mean by "not well defined". I believe
you said (in a previous post) that S is an infinite string of 1's. So,
what do you mean that the positions of S are not well defined?

It is impossible to discern the position of some digits. If only 1's
are involved, there is not much lost. But in case of numbers with
different digits, these numbers are not defined. (I used 0.111... only
because it easens the proof that irrational numbers are not well
defined.)

Regards, WM

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