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Prove that the set {1,2,3}xnatural numbers is countable.

Quote: Originally Posted by natewalker205 Prove that the set {1,2,3}xnatural numbers is countable. Hint: if $\displaystyle X = \{1,2,3\} \times \mathbb{N}, \text{consider } f:X \to \mathbb{N}$ defined as $\displaystyle f((i,n)) = 3(n-1)+i$ P.S: Though I have tailored this definition for this problem, any cartesian product of countable sets is countable