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# Parametric Operator

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Parametric Operator

In logic and mathematics, a parametric operator

Ω
with parameter
&al(ha;
in the parametric set
&Al(ha;
is a indexed_family of operators
(Ω&al(ha;)&Al(ha; = Ω&al(ha; : &al(ha; &isin; &Al(ha;
with index
&al(ha;
in the index set
&Al(ha;
.

Ω
is a parametric operator with parameter k in the set N of non-negative integers.

The application of a multigrade operator
Ω
to a finite sequence of operands (x1, â€¦, xk) is typically denoted with the parameter k left tacit, as the appropriate application is implicit in the number of operands listed. Thus
Ω
(x1, â€¦, xk) may be taken for
Ω
k(x1, â€¦, xk).

Some content adapted from the Pseudopedia article “Parametric operator” under the GNU Free Documentation License.
[ last updated: 7:26pm EDT - Sat, Apr 07 2007 ]
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