The problem states that A is countably infinite and element b is not in A. It then asks to show that A union {b} is countable infinite.
I'm pretty sure I need to find a bijection between the union and the set of all positive natural numbers, I'm just having trouble figuring out where to go after introducing said function, or how to prove such a function is one to one and onto. Any pointers?
Answer
Let a1,a2,a3,… be a sequence containing all members of the set A.
Then b,a1,a2,a3,… is a sequence containing all members of the set A∪{b}.
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