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What operation is denoted in e.g.:

$\Pi_{i \in I} S_i$

The document in question is:

John C. Reynolds - Types, abstraction, and parametric polymorphism

Since no index order is specified, the operation must be commutative and associative.

I am thinking that is means intersection, based on the idea that union is like addition, and intersection like multiplication. But I want to confirm it.

Thanks.

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1 Answer

up vote 8 down vote accepted

It usually stands for the cartesian product of the $S_i$, that is the set \[ \prod_{i\in I} S_i = \left\{f \colon I \to \bigcup_{i\in I} S_i \biggm| f(i) \in S_i \text{ for all } i \in I\right\} \]

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protected by Asaf Karagila Mar 9 '13 at 3:02

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