Prove that a union of any two countably infinite sets is countably infinite.
A union of any two countably infinite sets is countably infinite.
Disjoint union of finite set
be an infinite set.
Let be any countable infinite set.
Then there exist one-to-one, onto correspondence .
Let be countable infinite set.
To prove is countable infinite if .
Define a function as follows: for all integer .
The above function is one-to-one and onto.
Therefore, there exists one-to-one correspondence .
Hence, is countable infinite because set is countable infinite.
Therefore, the result stated in the question has been proved.
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