Re: An uncountable countable set

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.


Cardinality is a weak measure of size for infinite sets, the operative
word here being "measure".

It is a wrong measure. Cp. the vase.

Regards, WM


It is a non-measure, being only a rough and ill-founded classification.
.

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