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### Is the set of all pairs of natural numbers countable? [duplicate]

Say that $\Bbb N \times \Bbb N$ is the set of all pairs $(n_1, n_2)$ of natural numbers. Is it countable? My hypothesis is yes it is countable because sets are countable. But I am unable to come up ...
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### Union, intersection and Cartesian product of countable sets is countable [duplicate]

Possible Duplicate: Countable Sets and the Cartesian Product of them Sum of two countably infinite sets I want to solve a problem, this problem is the following: Prove that if the sets $A$ and ...
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### Show that $\mathbb{Q}\times \mathbb{Q}$ is denumerable [duplicate]

I am new to functions and relations, and with some concepts I am not so familiar. I have a question in an homework: Show that $\mathbb{Q} \times\mathbb{Q}$ is denumerable. From what I understood, ...
### Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
Using the definition of enumerability of sets: A non-empty set B is enumerable iff there is a bijection $f:\mathbb{N}\supset L \rightarrow B$. So, I have to prove that the set of polynomial of one ...