I am trying to represent the following set as the countable union of sets
$A = \{(x,y)|x<y\}$
I know that $A = \bigcup \{\{x|x<a\} \times \{y|a<y\}\}$ where $a$ is a real number
My problem is that I need to represent set $A$ using the countable union of sets using the cartesian product (as shown above), and in particular I need variable $a$ to be a function of natural numbers not reals. For example, $a$ can be $1/n$ where $n$ is a natural number ( this 1/n is wrong but I am just adding it for clarification).
Is such representation using natural numbers possible?