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Games For Arbitrarily Fat Rats

Workshop on Combinatorial Games, in honor of Elwyn Berlekamp's 75th Birthday November 01, 2015 - November 02, 2015

November 01, 2015 (11:30 AM PST - 12:15 PM PST)
Speaker(s): Aviezri Fraenkel (Weizmann Institute of Science)
Location: MSRI: Simons Auditorium
  • Diophantine approximation

  • fat rats

  • Dedekind cut

  • Wythoff's game

  • subtraction game

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC


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 (bn 1 + 
1c; : : : ; bn mc + 
mc) constitutes a complemen-
tary system of m sequences of integers if and only if i = (2m
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