MyWikiBiz, Author Your Legacy — Saturday October 05, 2024
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, 13:20, 6 January 2009
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| For brevity in the present case, and to serve as a generic device in any similar array of situations, let <math>S\!</math> be the type of an arbitrary sentence, possibly empty, and let <math>S'\!</math> be the type of a specifically non-empty sentence. In addition, let <math>\underline\varepsilon</math> be the type of the empty sentence, in effect, the language | | For brevity in the present case, and to serve as a generic device in any similar array of situations, let <math>S\!</math> be the type of an arbitrary sentence, possibly empty, and let <math>S'\!</math> be the type of a specifically non-empty sentence. In addition, let <math>\underline\varepsilon</math> be the type of the empty sentence, in effect, the language |
− | <math>\underline\varepsilon = \{ \varepsilon \}</math> that contains a single empty string, and let a plus sign "+" signify a disjoint union of types. In the most general type of situation, where the type <math>S\!</math> is permitted to include the empty string, one notes the following relation among types: | + | <math>\underline\varepsilon = \{ \varepsilon \}</math> that contains a single empty string, and let a plus sign <math>^{\backprime\backprime} + ^{\prime\prime}</math> signify a disjoint union of types. In the most general type of situation, where the type <math>S\!</math> is permitted to include the empty string, one notes the following relation among types: |
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| {| align="center" cellpadding="8" width="90%" | | {| align="center" cellpadding="8" width="90%" |