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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 19:48, 21 August 2012
, 19:48, 21 August 2012→6.14. Issue 3. The Status of Variables: markup
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<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}^{+\!\to} = (\underline{X} ~+\!\!\to \mathbb{B}) = \{ f : \underline{X} ~+\!\!\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><math>\underline{X}^{!\!\to} = (\underline{X} ~!\!\!\to \mathbb{B}) = \{ f : \underline{X} ~!\!\!\to \mathbb{B} \}.\!</math></p></li>
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d. The set of positive functions f : X >B has a cardinality of 2n and is notated as follows:
d. The set of positive functions f : X >B has a cardinality of 2n and is notated as follows: