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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