MyWikiBiz, Author Your Legacy — Tuesday November 26, 2024
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| Figure 24-2 illustrates the tacit extension of the proposition or scalar field <math>f = pq : X \to \mathbb{B}</math> to give the extended proposition or differential field that we notate as <math>\varepsilon f = \varepsilon (pq) : \operatorname{E}X \to \mathbb{B}.</math> | | Figure 24-2 illustrates the tacit extension of the proposition or scalar field <math>f = pq : X \to \mathbb{B}</math> to give the extended proposition or differential field that we notate as <math>\varepsilon f = \varepsilon (pq) : \operatorname{E}X \to \mathbb{B}.</math> |
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− | {| align="center" cellspacing="10" style="text-align:center; width:90%"
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− | <pre>
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− | o---------------------------------------------------------------------o
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− | | X |
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− | | o-------------------o o-------------------o |
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− | | / \ / \ |
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− | | / P o Q \ |
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− | | / / \ \ |
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− | | / / \ \ |
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− | | / / \ \ |
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− | | / / \ \ |
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− | | / / \ \ |
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− | | o o (dp) (dq) o o |
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− | | | | o-->--o | | |
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− | | | | \ / | | |
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− | | | (dp) dq | \ / | dp (dq) | |
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− | | | o<-----------------o----------------->o | |
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− | | | | | | | |
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− | | | | | | | |
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− | | | | | | | |
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− | | o o | o o |
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− | | \ \ | / / |
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− | | \ \ | / / |
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− | | \ \ | / / |
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− | | \ \ | / / |
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− | | \ \|/ / |
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− | | \ | / |
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− | | \ /|\ / |
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− | | o-------------------o | o-------------------o |
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− | | | |
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− | | dp | dq |
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− | | v |
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− | | o |
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− | o---------------------------------------------------------------------o
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− | Figure 24-2. Tacit Extension !e![pq] : EX -> B
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− | </pre>
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− | |}
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− | Thus we have a pictorial way of visualizing the following data:
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| {| align="center" cellspacing="10" style="text-align:center" | | {| align="center" cellspacing="10" style="text-align:center" |
| + | | [[Image:Field Picture PQ Tacit Extension Conjunction.jpg|500px]] |
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| + | | <math>\text{Figure 24-2. Tacit Extension}~ \varepsilon (pq) : \operatorname{E}X \to \mathbb{B}</math> |
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| <math>\begin{array}{rcccccc} | | <math>\begin{array}{rcccccc} |