  We define an extension of parity from the integers to the rational numbers.
Three parity classes are found -- even, odd and `none'. Using the 2-adic
valuation, we partition the rationals into subgroups with a rich algebraic
structure. The natural density provides a means of distinguishing the sizes of
countably infinite sets. The Calkin-Wilf tree has a remarkably simple parity
pattern, with the sequence `odd/none/even' repeating indefinitely. This pattern
means that the three parity classes have equal natural density in the
rationals. A similar result holds for the Stern-Brocot tree.
