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| | ==Note 13== | | ==Note 13== |
| | | | |
| − | <pre>
| + | I think that it ought to be clear at this point that we need a more systematic symbolic method for computing the differentials of logical transformations, using the term ''differential'' in a loose way at present for all sorts of finite differences and derivatives, leaving it to another discussion to sharpen up its more exact technical senses. |
| − | I think that it ought to be clear at this point that we | + | |
| − | need a more systematic symbolic method for computing the | + | For convenience of reference, let's recast our current example in the following form: |
| − | differentials of logical transformations, using the term | |
| − | "differential" in a loose way at present for all sorts of
| |
| − | finite differences and derivatives, leaving it to another | |
| − | discussion to sharpen up its more exact technical senses. | |
| | | | |
| − | For convenience of reference, let's recast our current
| + | {| align="center" cellpadding="8" width="95%" |
| − | example in the form F = <f, g> = <((u)(v)), ((u, v))>.
| + | | <math>F ~=~ (f, g) ~=~ ( ~\underline{((}~ u ~\underline{)(}~ v ~\underline{))}~, ~\underline{((}~ u ~,~ v ~\underline{))}~ ).</math> |
| | + | |} |
| | | | |
| | + | <pre> |
| | In their application to this logical transformation the operators | | In their application to this logical transformation the operators |
| | E and D respectively produce the "enlarged map" EF = <Ef, Eg> and | | E and D respectively produce the "enlarged map" EF = <Ef, Eg> and |