[ExI] a doubt concerning the h+ future
stathisp at gmail.com
Mon Jun 4 12:59:20 UTC 2007
On 04/06/07, John K Clark <jonkc at att.net> wrote:
The problem is that there are an infinite number of subsets that are just as
> large as the entire set, in fact, that is the very mathematical definition
> of infinity.
You're not obliged to constrain probability theory by that definition. The
cardinality of the set of odd numbers is the same as the cardinality of the
set of multiples of 10, but that doesn't mean that a randomly chosen integer
is just as likely to be odd as to be a multiple of 10; it is obviously 5
times as likely to be odd. Perhaps you can get around this by saying a
randomly chosen integer must be chosen from a finite set, otherwise it is
infinite, and infinity is not defined as either odd or a multiple of 10 or
neither. However, if there is an actual infinity of consecutively numbered
things, and you're in the middle of it, you can actually pick out a local
finite subset, and even though you might not know "where" it is in relation
to "zero" (if that is meaningful at all), you can be blindly sure that 5
times as many of the things will have a number ending in an odd integer as
in a zero.
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