# L7 - Generalized Unions/Intersections A union of a...

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Generalized Unions/Intersections A union of a collection of sets is the set that contains all elements that are members of at least one set in the collection. An intersection of a collection of sets is the set that contains all elements that are members of every set in the collection. 12 1 n ni i A A A A  1 n i A A A A 

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Example Let { , 1, 2,. ..} (infinite set) i A i i i 12 i.e. {1,2,3,. ..}, {2,3,4,. ..},. .. AA  1 1 {1,2,3,4,. ..} n i i 1 { , 2,. ..} n in i A n n n A and
A Few more Notations Summation Product 1 2 3 1 ... n ni i a a a a a 1 2 3 1 n i a a a a a   

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Climbing an Infinite Ladder If we: 1) Can get on the ladder 2) Know how to get from one rung to the next Then can we climb the entire ladder?
Mathematical Induction Mathematical Induction is a proof technique used to prove a statement that asserts that P(n) is true for all positive integers n .

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L7 - Generalized Unions/Intersections A union of a...

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