The enlargement operator <math>\operatorname{E},</math> also known as the ''shift operator'', has many interesting and useful properties in its own right, so let's examine a few of the more salient features that play out on the surface of our simple example, <math>f(x, y) = xy.\!</math>
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The enlargement operator E, also known as the "shift operator",
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has many interesting and very useful properties in its own right,
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so let us not fail to observe a few of the more salient features
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that play out on the surface of our simple example, f(x, y) = xy.
Introduce a suitably generic definition of the extended universe of discourse:
Introduce a suitably generic definition of the extended universe of discourse:
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Let U = X_1 x ... x X_k and EU = U x dU = X_1 x ... x X_k x dX_1 x ... x dX_k.
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Let <math>U = X_1 \times \ldots \times X_k</math> and <math>\operatorname{E}U = U \times \operatorname{d}U = X_1 \times \ldots \times X_k \times \operatorname{d}X_1 \times \ldots \times \operatorname{d}X_k.</math>