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Directory:Jon Awbrey/Papers/Differential Logic : Introduction (view source)
Revision as of 21:34, 16 June 2009
, 21:34, 16 June 2009→Note 25: segment text + set off graphics
style of differential field picture that we drew for the
style of differential field picture that we drew for the
tacit extension !e![pq] : EX -> B.
tacit extension !e![pq] : EX -> B.
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Figure 25-1. Enlargement E[pq] : EX -> B
Figure 25-1. Enlargement E[pq] : EX -> B
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A very important conceptual transition has just occurred here,
A very important conceptual transition has just occurred here,
almost tacitly, as it were. Generally speaking, having a set
almost tacitly, as it were. Generally speaking, having a set
mod 2, then the common loop drops out, leaving the 6 arrows of
mod 2, then the common loop drops out, leaving the 6 arrows of
D[pq] = !e![pq] + E[pq] that are illustrated in Figure 25-2.
D[pq] = !e![pq] + E[pq] that are illustrated in Figure 25-2.
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Figure 25-2. Difference Map D[pq] : EX -> B
Figure 25-2. Difference Map D[pq] : EX -> B
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The differential features of D[pq] may be collected cell by cell of
The differential features of D[pq] may be collected cell by cell of
the underlying universe X% = [p, q] to give the following expansion:
the underlying universe X% = [p, q] to give the following expansion: