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A multigrade operator $$\Omega\!$$ is a parametric operator with parameter $$k\!$$ in the set $$\mathbb{N}\!$$ 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 $$\Omega (x_1, \ldots, x_k)\!$$ may be taken for $$\Omega_k (x_1, \ldots, x_k).\!$$

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