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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.