Binary Operations

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defined by uv(x) = u(v(x)) for each x Î X. We shall refer to this operation as multiplication on F. The multiplication table is as follows:

This is an associative operation since function composition is associative. However, it is not commutative. The element g is a left and right identity. Note h and g are the only elements that have inverses and h is its own inverse as is g.Distributive PropertiesSuppose there are two binary operations and defined on a set A. We say that distributes over if for all a, b and c in A, and If we drop the circles around the plus and dot we get the familiar distributive law in the reals.

By Lance Jepsen

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