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Title:
Games For Arbitrarily Fat Rats
Speaker:
Abstract:
In kindergarten we learned about the integers (Peano axioms); in gram-
mar schhol { about pairs of integers (rationals); and then in high school,
about the reals (Dedekind cuts). Berlekamp, Conway, Guy discovered and
promoted a method (Don Knuth: \Surreal Numbers") of creating all of
those and much more { namely games! { in one masterful stroke.
Yet the rationals sometimes present obstinate diculties often over-
looked. Example. Let 1 < 1 <; : : : ;< m be real numbers, dubbed moduli ,
m 3. An over 40 years old conjecture states that there exist reals
i such
that the system (bn1 +
1c; : : : ; bnmc +
mc) constitutes a complemen-
tary system of m sequences of integers if and only if i = (2m
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