[FOM] throwing darts at natural numbers (reply to Arnon Avron)

Arnon Avron aa at tau.ac.il
Sun Aug 2 02:25:29 EDT 2009

On Thu, Jul 30, 2009 at 11:46:21PM -0400, Tom Dunion wrote:
> On Sunday, July 26, Arnon Avron wrote:
> >What will happen if our two heros throw darts at the natrural numbers
> >instead of the reals? It seems to me that by the same "argument"
> >we get that nothing could possoibly happen.
> The answer to the question is that A beats B,  50% of the time.


Well, believe it or not, but this is what will happen also
when your two friends throw darts at the real numbers between 0 and 1...
> The reason the previous argument (giving zero likelihood either player
> can win) does not go through is that it is impossible to assign a
> probability measure on the natural numbers without some being more
> likely to be "hit" than others.

So probability intuitions are not reliable in the countable case,
only in the uncountable one ... Well, 
if you are happy with this answer, and still maintains
that this "proof" of  CH is "intuitive", then there 
is no point in continuing the discussion. But try not to be surprised
by the fact that most people are not convinced by this "argument".

Arnon Avron

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