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I know how to handle the 2d case: http://www.proofwiki.org/wiki/Set_Difference_of_Cartesian_Products

But I am having trouble simplifying the following:

Let $X=\prod_{1}^\infty X_i, A_i \subset X_i$

How can I simplify/rewrite $X - (A_1 \times A_2 \times \cdots A_n \times X_{n+1} \times X_{n+2} \cdots)$ with unions/intersections?

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    Do you mean $A_i\in X_i$ or $A_i\subset X_i$?2011-02-18

2 Answers 2