Changes

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>

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}.

| <math>\prod_{i=1}^n X_i ~=~ X_1 \times \ldots \times X_n ~=~ \{ f : [n] \to \bigcup_{i=1}^n X_i ~|~ f(i) \in X_i \}.\!</math>

Viewing these functions as relations f c JxJxX, where X = Ui Xi,

Viewing these functions as relations <math>f \subseteq J \times J \times X,\!</math> where <math>X = \bigcup_{i=1}^n X_i\!</math> &hellip;

Another way to view these elements is as triples <math>i \widehat{~} j \widehat{~} x\!</math> such that <math>i = j\!</math> &hellip;

 

Another way to view these elements is as triples i^j^x such that i = j ???

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===6.35. Reducibility of Sign Relations===

===6.35. Reducibility of Sign Relations===