You need to specify the probability distribution by which the integers are selected. If the distribution is normalizable, e.g. p(n) = 1/2^n, thenthere's no paradox. But you seem to want a uniform distribution, p(n) = constant, and this does not exist. If p(n) = 0, then sum(p(n)) = 0, while if p(n) > 0, sum(p(n)) = infinity. The nonsensical nature of a uniform distribution over the integers can be realized by trying to devise a procedure for generating such integers. -- Gene
________________________________ From: Adam P. Goucher <apgoucher@gmx.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, June 5, 2011 7:20 AM Subject: [math-fun] Paradox
Select two random integers, a and b. Clearly, the probability of b being larger than a is 100%, as the expected value of b is infinite, yet the value of a is finite. Similarly, the probability of a being larger than b is 100%, by symmetry.
What have I done wrong?
Sincerely,
Adam P. Goucher
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