## Unary and Binary Ops

This page discusses unary and binary operations found in many Sets, Relations and Functions classes and also advanced Real Analysis.

unary operation
a mathematical function, say u, mapping a set S on to itself, i.e. $u:S \rightarrow S.$
binary operation
a procedure carried out on two numbers. In particular, it is a function that maps the cartesian product of two elements in a set on to itself, i.e. $S \times S \rightarrow S.$
algebraic structure
is a set, say S, along with a finite number of operations. Example: $\{ \mathbb{Z^{+}},- \}.$
closed or closed under
Let * be a binary operation on a set S. If $\forall a,b \in S_1,a*b \in S_1$ then $S_1$ is said to be closed under *.
commutative
a property of a binary operation, say *, on a set S such that $\forall a,b \in S, a*b=b*a.$
associative
a property of a binary operation * on a set S such that $\forall a,b,c \in S,a*(b*c)=(a*b)*c.$
idempotent
a property of a binary operation * on a set S such that $\forall a \in S, a*a=a.$ </dl>