1. How to prove(without combinatorics) that the set of all functions from {1,2,3,4,5} to {1,2,3} is finite ? (I think that the question asks for constructing a bijection from the set to $\{1,2,...,3^5\}$)
2. I can show that the set of all functions from {0,1} to $\mathbb{N}$ is countably infinite. The problem is I am not sure if the set of all functions from {1,2,3,4,5,...,n} where n is greater than or equal to 2 to $\mathbb{N}$ is countably infinite or uncountable. It seems far complicated than the preceding question.
Any hints or comments, please ? Thank you very much.
