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D_Alex comments on Open Thread, September 30 - October 6, 2013 - Less Wrong Discussion
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Hmm. What is the exact length of your, say, pen? Is it a rational number or a real number... I mean the EXACT lengh...?
Note if the answer to the last question is "it is a real number", then it is possible to construct the bet as proposed by the OP.
Before you quote "Planck's Length" in your reply, there is currently no directly proven physical significance of the Planck length (at least according to Wikipedia).