From owner-qed Fri Nov 4 06:41:50 1994
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Date: Fri, 04 Nov 1994 13:38:05
From: debruijn@win.tue.nl (N.G. de Bruijn)
To: jmc@sail.Stanford.EDU
Subject: Intuition about Freiling's axiom
Cc: qed@mcs.anl.gov
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To: John McCarthy
Cc: qed@mcs.anl.gov
Eindhoven, November 4, 1994.
I have not been able to see that the presentation of Freiling's
axiom you gave (in your email of 27 Oct 1994 to Dahn) makes it
"intuitive". In my opinion the probability argument is just one of
those paradoxes we so easily get by careless formulation of
probability statements. A simpler form of the same "paradox" is the
following one.
For every natural number x the probability that an arbitrary
natural number y happens to be less than x is zero. Now throw darts
on the natural numbers to determine x and y. The probability that y
is less than x is zero, and the probability that x is less than y is
zero. Nevertheless, the probability that at least one of x