In
mathematics, a
binary relation R on a
set X is
antisymmetric if there is no pair of distinct elements of
X each of which is related by
R to the other. More formally,
R is antisymmetric precisely if for all
a and
b in
X- if R(a,b) and R(b,a), then a = b,
or, equivalently,
- if R(a,b) with a ≠ b, then R(b,a) must not hold.