MyWikiBiz, Author Your Legacy — Monday November 25, 2024
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, 17:34, 18 January 2009
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| In order to deal with the higher order sign relations that are involved in this situation, I introduce a couple of new notations: | | In order to deal with the higher order sign relations that are involved in this situation, I introduce a couple of new notations: |
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− | # To mark the relation of denotation between a sentence <math>s\!</math> and the proposition that it denotes, let the ''underlined bracket'' notation <math>\underline{\lbrack} s \underline{\rbrack}</math> be used for ''the indicator function denoted by the sentence <math>s.\!</math>'' | + | # To mark the relation of denotation between a sentence <math>s\!</math> and the proposition that it denotes, let the ''floor'' notation <math>\lfloor s \rfloor</math> be used for ''the indicator function denoted by the sentence <math>s.\!</math>'' |
− | # To mark the relation of denotation between a proposition <math>p\!</math> and the set that it indicates, let the ''underlined brace'' notation <math>\underline{\lbrace} X \underline{\rbrace}</math> be used for ''the indicator function of the set <math>X.\!</math>'' | + | # To mark the relation of denotation between a proposition <math>p\!</math> and the set that it indicates, let the ''ceiling'' notation <math>\lceil X \rceil</math> be used for ''the indicator function of the set <math>X.\!</math>'' |
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− | Notice that the underlined bracket operator <math>\underline{\lbrack} ~ \underline{\rbrack}</math> takes one "downstream", in accord with the usual direction of denotation, from a sign to its object, while the underlined brace operator <math>\underline{\lbrace} ~ \underline{\rbrace}</math> takes one "upstream", against the usual direction of denotation, and thus from an object to its sign. | + | Notice that the floor operator <math>\lfloor ~ \rfloor</math> takes one "downstream", in accord with the direction of denotation, from a sign to its object, while the ceiling operator <math>\lceil ~ \rceil</math> takes one "upstream", against the direction of denotation, and thus from an object to its sign. |
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| In order to make these notations useful in practice, it is necessary to note of a couple of their finer points, points that might otherwise seem too fine to take much trouble over. For this reason, I express their usage a bit more carefully as follows: | | In order to make these notations useful in practice, it is necessary to note of a couple of their finer points, points that might otherwise seem too fine to take much trouble over. For this reason, I express their usage a bit more carefully as follows: |