MyWikiBiz, Author Your Legacy — Wednesday May 01, 2024
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, 03:42, 29 May 2009
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| ====Note 5==== | | ====Note 5==== |
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− | <pre>
| + | 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> |
− | The enlargement operator E, also known as the "shift operator", | |
− | has many interesting and very useful properties in its own right, | |
− | so let us not fail to observe a few of the more salient features | |
− | 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. | + | 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> |
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| + | <pre> |
| For a proposition f : X_1 x ... x X_k -> B, | | For a proposition f : X_1 x ... x X_k -> B, |
| the (first order) 'enlargement' of f is the | | the (first order) 'enlargement' of f is the |