Definition:Multigrade Operator

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 $$(x_1, \ldots, x_k)\!$$ is typically denoted with the parameter $$k\!$$ left tacit, as the appropriate application is implicit in the number of operands listed.

Thus $$\Omega (x_1, \ldots, x_k)\!$$ is taken to mean $$\Omega_k (x_1, \ldots, x_k)\!$$.