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Re: Distinguishability of paths of the Infinite Binary tree???
Posted:
Dec 26, 2012 3:43 AM
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On Dec 24, 12:42 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> There is nothing to happen "in the infinite". And it is completely
> irrelevant whether the paths after the distinction are finite or
> infinite. Everything that happens in a Cantor-list and in a Binary
> Tree happens at a finite level.
>
Up till now nobody have answered my question, anyhow. I still find it
puzzling really, Cantor has formally proved that there are more
distinguishable reals than are distinguishable finite initial segments
of them, I find that strange since the reals are only distinguishable
by those initial segments, so how they can be more than what makes
them distinguishable? This is too counter-intuitive!?
Probably this counter-intuitive issue is similar to the conflict
between distinguishability and the number of elements of a proper
subset and its set at infinite level, where the set would have
strictly more distinguishable elements than a proper subset of it and
yet they both have the SAME number of elements. So it appears to me
that the number of elements of infinite sets departs from the notion
of distinguishability.
I want to note that I'm not claiming to have paradox in the formal
sense, but there is a kind of extreme counter-intuitiveness involved
here with the notion of uncountability. Indeed this might drive some
to reject being involved with such concepts that would mess about our
intuitive faculaties and they would maintain that such slippery areas
of ideation are better avoided than engaged since they might be too
misleading. Anyhow
Zuhair
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