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, 20:48, 17 August 2012
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| <p>Associated with the coordinate space <math>\underline{X}\!</math> are various families of boolean-valued functions <math>f : \underline{X} \to \mathbb{B}.\!</math></p></li> | | <p>Associated with the coordinate space <math>\underline{X}\!</math> are various families of boolean-valued functions <math>f : \underline{X} \to \mathbb{B}.\!</math></p></li> |
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− | </ol> | + | <ol style="list-style-type:lower-latin"> |
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− | <pre> | + | <li> |
− | a. The set of all functions f : X >B has a cardinality of 22^n and is denoted as follows:
| + | <p>The set of all functions <math>f : \underline{X} \to \mathbb{B}\!</math> has a cardinality of <math>2^{2^n}\!</math> and is denoted as follows:</p> |
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| + | <p><math>\underline{X}^{\to} = (\underline{X} \to \mathbb{B}) = \{ f : \underline{X} \to \mathbb{B} \}.\!</math></p></li> |
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− | X-> = (X -> B) = {f : X -> B}.
| + | </ol></ol> |
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| + | <pre> |
| b. The set of linear functions f : X >B has a cardinality of 2n and is known as the "dual space" X* in vector space contexts. In formal language contexts, in order to avoid conflicts with the use of the "Kleene star" operator, it needs to be given an alternate notation: | | b. The set of linear functions f : X >B has a cardinality of 2n and is known as the "dual space" X* in vector space contexts. In formal language contexts, in order to avoid conflicts with the use of the "Kleene star" operator, it needs to be given an alternate notation: |
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