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Directory:Jon Awbrey/Papers/Inquiry Driven Systems (view source)
Revision as of 04:16, 19 January 2009
, 04:16, 19 January 2009→1.3.10.7. Stretching Operations: mathematical markup
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In particular, one observes the following relations and formulas:
In particular, one can observe the following relations and formulas, all of a purely notational character:
1. If the sentence S denotes the proposition P : U -> B, then [S] = P.
:{| cellpadding="4"
| valign="top" | 1.
| colspan="3" | Let the sentence <math>s\!</math> denote the proposition <math>q,\!</math>
|-
| || || where
| <math>q : X \to \underline\mathbb{B}.</math>
|-
|
| colspan="3" | Then we have the notational equivalence:
|-
| ||
| colspan="2" | <math>\downharpoonleft s \downharpoonright ~=~ q.</math>
|-
| valign="top" | 2.
| colspan="3" | Let the sentence <math>s\!</math> denote the proposition <math>q,\!</math>
|-
| || || where
| <math>q : X \to \underline\mathbb{B}</math>
|-
| || || and
| <math>[| q |] ~=~ q^{-1} (\underline{1}) ~=~ Q \subseteq X.</math>
|-
|
| colspan="3" | Then we have the notational equivalences:
|-
| ||
| colspan="2" | <math>\downharpoonleft s \downharpoonright ~=~ q ~=~ f_Q ~=~ \upharpoonleft Q \upharpoonright.</math>
|}
<pre>
3. X = {u C U : u C X}
3. X = {u C U : u C X}
= |{X}| = {X}-1(1)
= |{X}| = {X}-1(1)
= |fX| = fX-1(1).
= |fX| = fX-1(1).
4. {X} = { {u C U : u C X} }
4. {X} = { {u C U : u C X} }