, nor 
holds. The
book gives an example of 
which can't be compared
directly to n because it often acts like 
.
The ``big'' and ``little'' functions behave almost exactly like their standard real-number counterparts: transitivity, reflexivity, symmetry, and transpose symmetry.
However, one standard property does not hold: trichotomy. There
are pairs of functions f(n) and g(n) such that none of f(n) =
o(g(n)), , nor holds. The
book gives an example of which can't be compared
directly to n because it often acts like .
