The associativity equation or associativity functional equation is the functional equation F ( F ( x , y ) , z ) = F ( x , F ( y , z ) ) {\displaystyle F(F(x,y),z)=F(x,F(y,z))} for a function F : X × X → X {\displaystyle F\colon X\times X\to X} . It characterizes those binary operations F {\displaystyle F} on a set X {\displaystyle X} that are associative in the usual algebraic sense, and therefore underlies the study of semigroups and many kinds of aggregation operators.
The associativity equation or associativity functional equation is the functional equation F ( F ( x , y ) , z ) = F ( x , F ( y , z ) ) {\displaystyle F(F(x,y),z)=F(x,F(y,z))} for a function F : X × X → X {\displaystyle F\colon X\times X\to X} . It characterizes those binary operations F {\displaystyle F} on a set X {\displaystyle X} that are associative in the usual algebraic sense, and therefore underlies the study of semigroups and many kinds of aggregation operators.
Source: Wikipedia "Associativity equation" · CC BY-SA 4.0
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