I'm reading the text about the proof of Z and Q are countable.
The proof reads:
is the union of the countable sets , and one can define a surjection by if and
End of proof.
I understand that basically the system of Z and Q are equivalent, so if Z is countable so is Q, but where in the proof did it show that there exist an injection from Z to the set of natural numbers? Thanks.
There's a theorem to the effect that the union of a countable number of countable sets is itself countable:
Union of Countable Sets - ProofWiki