Re: Different Kinds of Infinity

On Aug 5, 10:18 pm, "R. Baldwin" <res0k...@xxxxxxxxxxxxxxxxxxxx>
wrote:

There really are different kinds ofinfinity, some bigger than others.
But the rest of the paragraph is quite meaningless. Those categories
don't apply to this situation.

Yeah, I know about Cantor, C, Aleph Null etc but I can't see where
these apply here

The context had to do with where the output of an algorithm might match a
subsequence in a normal number.Infinityin this circumstance corresponds to
the cardinality of the natural numbers, so only Aleph Null would apply.

That's right . . .

I guess the term "different characteristics" or "features" would be a
better term to use when it comes to comparing different aleph-null
infinities - since they are technically the same "size".

The point is that, depending upon the different characteristics or
features of numbers in different infinite sets, certain sets are
easier to select, at random, than others. Although different aleph-
null sets have "equal size", they do not have equal probability of a
member being "selected" at random. The odds of selection decrease as
the size of the specific finite sequence in question increases - even
though this specific sequence is part of an infinite aleph-null set of
such sequences. The odds that anything in this infinite set will
actually be chosen decreases exponentially with the size of the
specific sequence in question.

Sean Pitman
www.DetectingDesign.com


.

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