Why are pushdown automata countable? I began a chapter in a textbook on computational theory where they begin to talk about decidable languages. 

The problems in this section are pretty confusing and I honestly don't know how to begin them because I'm not 100% on what they mean when they say "countable". 

Can anyone help walk me through this problem in the book, that simply states;


  Show that the number of push-down automatons is countable.
Since you don't provide any attempt on your own part, note two things.


The definition of countability.


  A set $A$ is countable if and only if $A$ is finite or there is a bijection $f : A \to \mathbb{N}$.

How do you represent pushdown automata in a formal way?


If you digest the first item and answer the second, the answer should become apparent.