Because the data
a and
b are unconstrained, the ordering
O has
to be what is known as a
total ordering, so that for any two values
a and
b, at least one of
O(
a,
b) or
O(
b,
a) produces
true. The alternative is called a
partial order, in which both of
O(
a,
b) or
O(
b,
a) produces false.
The ≤ ordering over integers is a total ordering. The <
ordering over integers is a partial ordering; if a = b, then neither
a < b nor b < a is true (< is a total ordering in the
presence of a collection of unique integers).
This page last modified on 24 January 2006.