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MyWikiBiz, Author Your Legacy — Thursday June 27, 2024
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==Note 22==
 
==Note 22==
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<pre>
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Let us summarize, in rough but intuitive terms, the outlook on differential logic that we have reached so far. We've been considering a class of operators on universes of discourse, each of which takes us from considering one universe of discourse, <math>X^\circ,</math> to considering a larger universe of discourse, <math>\operatorname{E}X^\circ.</math>
It would be good to summarize, in rough but intuitive terms,
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the outlook on differential logic that we have reached so far.
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We've been considering a class of operators on universes
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An operator <math>\operatorname{W}</math> of this general type, namely,<math>\operatorname{W} : X^\circ \to \operatorname{E}X^\circ,</math> acts on each proposition <math>f : X \to \mathbb{B}</math> of the source universe <math>X^\circ</math> to produce a proposition <math>\operatorname{W}f : \operatorname{E}X \to \mathbb{B}</math> of the target universe <math>\operatorname{E}X^\circ.</math>
of discourse, each of which takes us from considering one
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universe of discourse, X%, to considering a larger universe
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of discourse, EX%.
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Each of these operators, in broad terms having the form
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The two main operators that we have worked with up to this point are the enlargement or shift operator <math>\operatorname{E} : X^\circ \to \operatorname{E}X^\circ</math> and the difference operator <math>\operatorname{D} : X^\circ \to \operatorname{E}X^\circ.</math>
W : X% -> EX%, acts on each proposition f : X -> B of the
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source universe X% to produce a proposition Wf : EX -> B
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of the target universe EX%.
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The two main operators that we have worked with up to this
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point are the enlargement or shift operator E : X% -> EX%
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and the difference operator D : X% -> EX%.
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<pre>
 
E and D take a proposition in X%, that is, a proposition f : X -> B
 
E and D take a proposition in X%, that is, a proposition f : X -> B
 
that is said to be "about" the subject matter of X, and produce the
 
that is said to be "about" the subject matter of X, and produce the
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