# countability of the subset of cartesian product of integers [duplicate]

Let us consider the set $$X$$ of the following infinite dimensional vectors:

$$x = (x_{1}, x_{2}, \dots, x_{k}, 0, \dots,),$$ such that $$x_{i} \in \mathbb{Z}$$ and for any $$x$$ there exist $$k < \infty$$ such that $$x_{j} = 0$$ for all $$j > k$$.

The statement: $$X$$ is not countable.

Try: I tried to show this using the fact that the set of all subsets of all integers is uncountable

• awesome! I see now! yes, $X$ can be any countable set. – ABK Oct 29 '19 at 16:03