Prove that these sets are countable :
A. Set of relations over natural which is composed by exactly one ordered pair.
B. Set of relations over natural composed by finite number of ordered pairs.
thanks.
Prove that these sets are countable :
A. Set of relations over natural which is composed by exactly one ordered pair.
B. Set of relations over natural composed by finite number of ordered pairs.
thanks.
The set A is essentially the collection of all singletons from the set $\mathbb{N}\times\mathbb{N}$. (Can you see why?) So the question is: can you prove that $\mathbb{N}\times\mathbb{N}$ is countable?
The second set is the collection of all finite subsets of $\mathbb{N}\times\mathbb{N}$. Perhaps you can prove that that the set of all subsets of a given finite size is countable, and then take a union?