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Given the indexed collection of denumerable sets A_i with i N, prove that their union U_i N
A_i is also denumerable.
Solution
Given Ai is the denumerable sets
Union represents combination of all elements in all the sets
Hence U Ai has infinite many sets as Ai alone has infinite many sets
Hence U Ai is also denumerable

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Given the indexed collection of denumerable sets A_i with i N, prov.pdf

  • 1. Given the indexed collection of denumerable sets A_i with i N, prove that their union U_i N A_i is also denumerable. Solution Given Ai is the denumerable sets Union represents combination of all elements in all the sets Hence U Ai has infinite many sets as Ai alone has infinite many sets Hence U Ai is also denumerable