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Construction of Numerical Functions
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a o a a o b a o c additive conjoint structure additive representation algebra algebra of sets Archimedean axiom Archimedean property assume assumption Ax x A2 axiomatization axioms of Definition b o c binary operation binary relation Chapter component concatenation conditional probability construct countable defined denote dimensional analysis elements empirical entropy Equation equivalence classes equivalence relation essential maximum example exists extensive measurement extensive structure finite formulate function f hence holds hypothesis implies independent indifference curves inequalities integer interval scale laws minimal element monotonicity multiplicative order preserving pairs polynomial proof of Theorem prove qualitative probability ratio scale real numbers real-valued function relational structure representation theorem restricted solvability result Section semigroup sign dependence simple order solution strictly increasing structure of qualitative subset Suppose theory Thomsen condition transformations utility variables vector velocity weak order yields