Re: An uncountable countable set


Tony Orlow schrieb:

mueckenh@xxxxxxxxxxxxxxxxx wrote:
Tony Orlow schrieb:


Why not? Each and every number of the list terminates. That one is a number
that does *not* terminate.

> If you think that 0.111... is a number, but not in the list,

It is me who insists that it is not a representation of a number.
Well, Wolfgang, that sets us apart, though I agree it's not a "specific"
number. It's still some kind of quantitative expression, even if it's
unbounded. Would you agree that ...333>...111, given a digital number
system where 3>1?

That is the similar to 0.333... > 0.111.... But all these
representations exist only potentially, in my opinion. The difference
is, that 0.333... can be shown to lie between two existing numbers, so
we can calculate with it, while for ...333 this cannot be shown.

I think it can be shown to lie between ...111 and ...555, given that
each digit is greater than the corresponding digit in the first, and
less than the corresponding digit in the second.

Yes, but only if we define, for instance,

A n eps |N : 111...1 < 333...3 where n digits are symbolized in both
cases.

This approach would be comparable with the "measure" which gives

A n eps |N : |{1,2,3,...,2n}| = 2*|{2,4,6,...,2n}|.

I don't know whether these definitions are of any use, but I am sure
that they are not less useful than Cantor's cardinality.

Regards, WM

..

.

Relevant Pages

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