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Revision as of 14:52, 18 January 2009
, 14:52, 18 January 2009→1.3.10.7. Stretching Operations: mathematical markup
The preceding discussion of stretch operations is slightly more general than is called for in the present context, and so it is probably a good idea to draw out the particular implications that are needed right away.
The preceding discussion of stretch operations is slightly more general than is called for in the present context, and so it is probably a good idea to draw out the particular implications that are needed right away.
If <math>F : \underline\mathbb{B}^k \to \underline\mathbb{B}</math> is a boolean function on <math>k\!</math> variables, then it is possible to define a mapping <math>F^\$ : (X \to \underline\mathbb{B})^k \to (X \to \underline\mathbb{B}),</math> in effect, an operation that takes <math>k\!</math> propositions into a single proposition, where <math>F^\$</math> satisfies the following conditions:
<pre>
<pre>
F$(f1, ..., fk) : U -> B
F$(f1, ..., fk) : U -> B
:
:
F$(f1, ..., fk)(u) = F(f(u))
F$(f1, ..., fk)(u) = F(f(u))
