Projection operation

Remarks

Example: on $A = \Z$, the operation $\pi^2_1(a, b) = a$ is a projection; it returns the first of its two arguments for every input. Non-example: on $\Z$, the operation $(a, b) \mapsto \max(a, b)$ is not a projection, since $\max(1, 0) = 1 \ne 0$ rules out $\pi^2_2$ and $\max(0, 1) = 1 \ne 0$ rules out $\pi^2_1$. The unary projection $\pi^1_1$ is the identity map of $A$. In any algebra with universe $A$, the term $x_k$, read as a term in the variables $x_1, \dots, x_n$, has the term operation $\pi^n_k$.