How do I go about showing that the cardinality of the set of natural numbers and the cardinality of the cartesian product of integers is the same?:
$$|\Bbb N|=|\Bbb Z \times \Bbb Z|$$
Directly $|\Bbb N| = \aleph_0$ and I can separate the right side like this: $|\Bbb Z||\Bbb Z|$, and because the cardinality of the set of integers is $\aleph_0$, $\aleph_0$ times $\aleph$ is still $\aleph_0$ and thus they are equal. However, I need to show an example how a bijection can be used here? How do I construct a map to let me see a bijection is being used/provide that it is surjective/injective?