Changes

Directory:Jon Awbrey/Papers/Inquiry Driven Systems (view source)

Revision as of 14:52, 18 January 2009

144 bytes added , 14:52, 18 January 2009

→‎1.3.10.7. Stretching Operations: mathematical markup

Line 3,139: Line 3,139:

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>

−

If F : Bk -> B is a boolean function on k variables, then it is possible to define a mapping F$ : (U -> B)k -> (U -> B), in effect, an operation that takes k propositions into a single proposition, where F$ satisfies the following conditions:

+

F$(f1, ..., fk) : U -> B

−

F$(f1, ..., fk) : U -> B

:

F$(f1, ..., fk)(u) = F(f(u))

Jon Awbrey

12,080

edits