Operations (mathematics)
The most common operations are addition and multiplication of real numbers. For example, in addition we have $3+2=5$, which implies that with an ordered pair of numbers $(3,2)$, it associates the number $5$. By observing this property, we can define operations in a general set-theoretic setting.
Definitions
Let $S$ be a set.
A $n$-ary operation on $S$ is a map $S^{n}=\underbrace{S\times S\times\cdot\cdot\cdot\times S}_{n}\rightarrow S$ from the Cartesian product $S^{n}$ to $S$. Here the integer $n$ is called the arity of the operation.
Next, consider the special cases when $n\in\{0,1,2\}$.
A binary operation on $S$ is a map $S^{2}=S\times S\rightarrow S$. A unary operation on $S$ is a map $S^{1}=S\rightarrow S$ from $S$ to itself. A nullary operation or constant operation on $S$ is a map $S^{0}=*\rightarrow S$, where $*$ denotes a singleton set.
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