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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 21:00, 21 August 2012
, 21:00, 21 August 2012→6.14. Issue 3. The Status of Variables: markup
<p>The set of ''linear functions'' <math>f : \underline{X} \to \mathbb{B}\!</math> has a cardinality of <math>2^n\!</math> and is known as the ''dual space'' <math>\underline{X}^{*}\!</math> 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:</p>
<p>The set of ''linear functions'' <math>f : \underline{X} \to \mathbb{B}\!</math> has a cardinality of <math>2^n\!</math> and is known as the ''dual space'' <math>\underline{X}^{*}\!</math> 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:</p>
<p><math>\underline{X}^{+\!\to} = (\underline{X} ~+\!\!\to \mathbb{B}) = \{ f : \underline{X} ~+\!\!\to \mathbb{B} \}.\!</math></p></li>
<p><math>\underline{X}^{\oplus\!\to} = (\underline{X} ~\oplus\!\!\to \mathbb{B}) = \{ f : \underline{X} ~\oplus\!\!\to \mathbb{B} \}.\!</math></p></li>
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<p>The set of ''singular functions'' <math>f : \underline{X} \to \mathbb{B}\!</math> has a cardinality of <math>2^n\!</math> and is notated as follows:</p>
<p>The set of ''positive functions'' <math>f : \underline{X} \to \mathbb{B}\!</math> has a cardinality of <math>2^n\!</math> and is notated as follows:
<p><math>\underline{X}^{!\!\to} = (\underline{X} ~!\!\!\to \mathbb{B}) = \{ f : \underline{X} ~!\!\!\to \mathbb{B} \}.\!</math></p></li>
<p><math>\underline{X}^{\otimes\!\to} = (\underline{X} ~\otimes\!\!\to \mathbb{B}) = \{ f : \underline{X} ~\otimes\!\!\to \mathbb{B} \}.\!</math></p></li>
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<p>The set of ''positive functions'' <math>f : \underline{X} \to \mathbb{B}\!</math> has a cardinality of <math>2^n\!</math> and is notated as follows:
<p>The set of ''singular functions'' <math>f : \underline{X} \to \mathbb{B}\!</math> has a cardinality of <math>2^n\!</math> and is notated as follows:</p>
<p><math>\underline{X}^{\otimes\!\to} = (\underline{X} ~\otimes\!\!\to \mathbb{B}) = \{ f : \underline{X} ~\otimes\!\!\to \mathbb{B} \}.\!</math></p></li>
<p><math>\underline{X}^{\odot\!\to} = (\underline{X} ~\odot\!\!\to \mathbb{B}) = \{ f : \underline{X} ~\odot\!\!\to \mathbb{B} \}.\!</math></p></li>
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