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Combinatorial game theory
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===Up and down=== ''Up'', written as β, is a position in combinatorial game theory.<ref name=winningways>{{cite book |author1=E. Berlekamp |author2=J. H. Conway |author3=R. Guy | title=[[Winning Ways for your Mathematical Plays]] | volume=I | publisher=Academic Press | year=1982 | isbn=0-12-091101-9}}<br />{{cite book |author1=E. Berlekamp |author2=J. H. Conway |author3=R. Guy | title=Winning Ways for your Mathematical Plays | volume=II | publisher=Academic Press | year=1982 | isbn=0-12-091102-7}}</ref> In standard notation, β = {0|β}. Its negative is called ''down''. : ββ = β (''down'') Up is strictly positive (β > 0), and down is strictly negative (β < 0), but both are [[infinitesimal]]. Up and down are defined in ''[[Winning Ways for your Mathematical Plays]]''.
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