1) a) Prove that the union of two countable sets is
countable.
b) Prove that the union...
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Advance Math
1) a) Prove that the union of two countable sets iscountable.
b) Prove that the union of a finite collection of countable setsis countable.
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a Let A and B be countable sets We will consider four cases case 1 Suppose both A and B are finite Then A B is finite and hence countable case 2 Suppose one of A and B is finite and the other is countably infinite Assume without loss of generality that A is finite Since B is countably infinite there exists a function f B 7 Z which is a
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