Multigrade operator

In logic and mathematics, a multigrade operator $\Omega$ is a parametric operator with parameter k in the set N of non-negative integers.

The application of a multigrade operator $\Omega$ to a finite sequence of operands (x₁, …, x_k) is typically denoted with the parameter k left tacit, as the appropriate application is implicit in the number of operands listed. Thus $\Omega$ (x₁, …, x_k) may be taken for $\Omega$ _k(x₁, …, x_k).