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Topic: Wikipedia definition of pi system is self-contradictory -- please
help me clarify.

Replies: 3   Last Post: Jul 10, 2014 4:01 AM

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Paul

Posts: 434
Registered: 7/12/10
Wikipedia definition of pi system is self-contradictory -- please
help me clarify.

Posted: Jul 9, 2014 7:13 PM
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The wikipedia defines a pi-system on a set omega as being a collection P of subsets of omega such that P is non-empty and such that A intersect B belongs to P whenever A and B belong to P.

However, the article goes on to give another definition that contradicts the previous one -- namely "That is, P is a non-empty family of subsets of omega that is closed under finite intersections."

These are different definitions. The empty intersection of subsets of omega = omega. Therefore the set omega is required to belong to P under the second definition, but need not do so under the first definition.

Does anyone know whether omega is required to belong to P or is the definition not completely standardised?

Thank You,

Paul Epstein



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