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Revision as of 21:30, 16 June 2009
, 21:30, 16 June 2009→Note 24: segment text + set off graphics
as a scalar field, in effect, a potential "plateau" of elevation 1
as a scalar field, in effect, a potential "plateau" of elevation 1
over the shaded region, with an elevation of 0 everywhere else.
over the shaded region, with an elevation of 0 everywhere else.
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Figure 24-1. Proposition pq : X -> B
Figure 24-1. Proposition pq : X -> B
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Given any proposition f : X -> B, the "tacit extension" of f to EX
Given any proposition f : X -> B, the "tacit extension" of f to EX
is notated !e!f : EX -> B and defined by the equation !e!f = f, so
is notated !e!f : EX -> B and defined by the equation !e!f = f, so
or scalar field f = pq : X -> B to give the extended proposition
or scalar field f = pq : X -> B to give the extended proposition
or differential field that we notate as !e!f = !e![pq] : EX -> B.
or differential field that we notate as !e!f = !e![pq] : EX -> B.
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Figure 24-2. Tacit Extension !e![pq] : EX -> B
Figure 24-2. Tacit Extension !e![pq] : EX -> B
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Thus we have a pictorial way of visualizing the following data:
Thus we have a pictorial way of visualizing the following data:
