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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)

Revision as of 16:34, 19 August 2012

200 bytes added , 16:34, 19 August 2012

→‎6.14. Issue 3. The Status of Variables: markup

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<math>\underline{X}^{\to} = (\underline{X} \to \mathbb{B}) = \{ f : \underline{X} \to \mathbb{B} \}.\!</math></li>

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<li>

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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:

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<math>\underline{X}^{+\!\to} = (\underline{X} +\!\!\to \mathbb{B}) = \{ f : \underline{X} +\!\!\to \mathbb{B} \}.\!</math></li>

</ol></ol>

<pre>

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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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~~X+> = (X +> B) = {f : X +> B}.~~

c. The set of singular functions f : X >B has a cardinality of 2n and is notated as follows:

Jon Awbrey

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