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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 00:45, 13 February 2013
, 00:45, 13 February 2013→6.34. Set-Theoretic Constructions: markup
| <math>\prod_{i=1}^n X_i ~=~ X_1 \times \ldots \times X_n ~=~ \{ (x_1, \ldots, x_n) : x_i \in X_i \}.\!</math>
| <math>\prod_{i=1}^n X_i ~=~ X_1 \times \ldots \times X_n ~=~ \{ (x_1, \ldots, x_n) : x_i \in X_i \}.\!</math>
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As an alternative definition, the <math>n\!</math>-tuples of <math>\prod_{i=1}^n X_i\!</math> can be regarded as sequences of elements from the successive <math>X_i\!</math> and thus as functions that map <math>[n]\!</math> into the sum of the <math>X_i,\!</math> namely, as the functions <math>f : [n] \to \bigcup_{i=1}^n X_i\!</math> that obey the condition <math>f(i) \in i \widehat{~} X_i.\!</math>
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Xi Xi = X1 x ... x Xn = { f : [n] > Ui Xi | f(i) C Xi for all i}.
Xi Xi = X1 x ... x Xn = { f : [n] > Ui Xi | f(i) C Xi for all i}.