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Let n ∈ Z^+ and denote by N^n =N×N×...×N (n times). Prove that N^n is countable...

Let n ∈ Z^+ and denote by N^n =N×N×...×N (n times). Prove that N^n is countable for all n ∈Z+.

Please answer questions in clear hand-writing and show me the full process, thank you (Sometimes I get the answer which was difficult to read).

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Answer #1

A set p is said to be countable, if I a one-one mapping f sit. I f : P N The set of natural numbeil Now let us desire a functEvery natural number has a unique representation of product of prime numbers(with power)

p1,p2,... ,pn be the 1st n prime numbers.

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