One may assume that the rational numbers are contained in the field.
In fact, this particular interpretation is often used to define the rational numbers.
Therefore the square root of 2 cannot be a rational number.
A simple example is the set of non-zero rational numbers.
The same sign rules apply to rational and real numbers.
F is a field of characteristic 0, usually the rational numbers.
Therefore every positive rational number appears exactly once in this tree.
There is a Ford circle associated with every rational number.
In this way, we produce an infinite list with all the rational numbers.
The choice (the field of rational numbers) and is suitable.