Find solution
What if union of disjoint sets results in universal set?

Prove that the union of all the sets in the sequence is a countable set.?

  • Answer:

    As A1, A2, etc., are countable, there exist injective functions f1:A1→N, f2:A2→N, etc. Then there exists an injective function g:A1UA2U...→NxNx... . As there exists an injective function h:NxNx...→N, then h∘g:A1UA2U...→N is injective as well. Hence, the union of all sets in a sequence of countable sets is itself countable.

questiongirl at Yahoo! Answers Visit the source

Was this solution helpful to you?

Other answers

As A1, A2, etc., are countable, there exist injective functions f1:A1→N, f2:A2→N, etc. Then there exists an injective function g:A1UA2U...→NxNx... . As there exists an injective function h:NxNx...→N, then h∘g:A1UA2U...→N is injective as well. Hence, the union of all sets in a sequence of countable sets is itself countable.

s k

Related Q & A:

Just Added Q & A:

Find solution

For every problem there is a solution! Proved by Solucija.

  • Got an issue and looking for advice?

  • Ask Solucija to search every corner of the Web for help.

  • Get workable solutions and helpful tips in a moment.

Just ask Solucija about an issue you face and immediately get a list of ready solutions, answers and tips from other Internet users. We always provide the most suitable and complete answer to your question at the top, along with a few good alternatives below.