  In this article, we introduce a new object, a virtual quadratic space, and
its group of isometries. They are presented as natural generalizations of
quadratic spaces and orthogonal groups. It is then shown that by replacing
quadratic spaces with virtual quadratic spaces, we can unify certain
enumerative properties of finite fields, without distinguishing between even
and odd characteristics, such as the number of non-isomorphic non-degenerate
quadratic forms, and the order of groups of isometries.
