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Associative


Three elements x, y and z of a set S are said to be associative under a binary operation * if they satisfy

 x*(y*z)=(x*y)*z.
(1)

Real numbers are associative under addition

 x+(y+z)=(x+y)+z
(2)

and multiplication

 x·(y·z)=(x·y)·z.
(3)

The Wolfram Language attribute that sets a function to be associative is Flat.


See also

Associative Algebra, Commutative, Distributive, Transitive Explore this topic in the MathWorld classroom

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Cite this as:

Weisstein, Eric W. "Associative." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Associative.html

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