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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 13:33, 27 April 2009
, 13:33, 27 April 2009→Commentary Note 12.2
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| <math>\begin{matrix}Y^X & = & (X \to Y) & = & \{f : X \to Y \}\end{matrix}</math>
| <math>\begin{matrix}Y^X & = & (X \to Y) & = & \{ f : X \to Y \}\end{matrix}</math>
|}
|}
| <math>\begin{matrix}|Y^X| & = & |Y|^{|X|}\end{matrix}</math>
| <math>\begin{matrix}|Y^X| & = & |Y|^{|X|}\end{matrix}</math>
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In the special case where <math>Y = \mathbb{B} = \{ 0, 1 \},</math> the function space <math>\mathbb{B}^X</math> is the set of functions <math>\{ f : X \to \mathbb{B} \}.</math> If the elements <math>0, 1 \in \mathbb{B}</math> are interpreted as the logical values <math>\operatorname{false}, \operatorname{true},</math> respectively, then a function of the type <math>X \to \mathbb{B}</math> may be interpreted as a ''proposition'' about the elements in <math>X.\!</math>
==References==
==References==