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Revision as of 14:47, 19 January 2009
, 14:47, 19 January 2009→1.3.10.7. Stretching Operations: math markup + typo fixes
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| valign="top" | 3.
| valign="top" | 3.
| <math>X\!</math>
| align="center" | <math>Q\!</math>
| align="center" | <math>=\!</math>
| align="center" | <math>=\!</math>
| <math>\{ x \in X : x \in Q \}</math>
| <math>\{ x \in X : x \in Q \}</math>
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| align="center" | <math>=\!</math>
| align="center" | <math>=\!</math>
| <math>[| \upharpoonleft X \upharpoonright |] \quad = \quad \upharpoonleft X \upharpoonright^{-1} (\underline{1})</math>
| <math>[| \upharpoonleft X \upharpoonright |] ~=~ \upharpoonleft X \upharpoonright^{-1} (\underline{1})</math>
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| align="center" | <math>=\!</math>
| align="center" | <math>=\!</math>
| <math>[| f_Q |] \quad = \quad f_Q^{-1} (\underline{1}).</math>
| <math>[| f_Q |] ~=~ f_Q^{-1} (\underline{1}).</math>
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| valign="top" | 4.
| align="center" | <math>\upharpoonleft Q \upharpoonright</math>
| align="center" | <math>=\!</math>
| <math>\upharpoonleft \{ x \in X : x \in Q \} \upharpoonright</math>
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| align="center" | <math>=\!</math>
| <math>\downharpoonleft x \in Q \downharpoonright</math>
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| align="center" | <math>=\!</math>
| <math>f_Q.\!</math>
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<pre>
<pre>
Now if a sentence S really denotes a proposition P, and if the notation "[S]" is merely meant to supply another name for the proposition that S already denotes, then why is there any need for the additional notation? It is because the interpretive mind habitually races from the sentence S, through the proposition P that it denotes, and on to the set X = P-1(1) that the proposition P indicates, often jumping to the conclusion that the set X is the only thing that the sentence S is intended to denote. This HO sign situation and the mind's inclination when placed within its setting calls for a linguistic mechanism or a notational device that is capable of analyzing the compound action and controlling its articulate performance, and this requires a way to interrupt the flow of assertion that typically takes place from S to P to X.
Now if a sentence S really denotes a proposition P, and if the notation "[S]" is merely meant to supply another name for the proposition that S already denotes, then why is there any need for the additional notation? It is because the interpretive mind habitually races from the sentence S, through the proposition P that it denotes, and on to the set X = P-1(1) that the proposition P indicates, often jumping to the conclusion that the set X is the only thing that the sentence S is intended to denote. This HO sign situation and the mind's inclination when placed within its setting calls for a linguistic mechanism or a notational device that is capable of analyzing the compound action and controlling its articulate performance, and this requires a way to interrupt the flow of assertion that typically takes place from S to P to X.
</pre>
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