Inequality symbol
There are four symbols conventionally used to represent the notion of inequality.
If and
are real numbers we write:
to mean that
is strictly greater than
(that is,
cannot equal
).
to mean that
is greater than or equal to (equivalently, "at least as large as")
.
to mean that
is strictly less than
to mean that
is less than or equal to
.
We use a slash through an inequality symbol to represent that the given inequality does not hold. Thus for real numbers and
,
if and only if
if and only if
if and only if
if and only if
if and only if
or
These symbols are also frequently used to represent the order relation in a partially ordered set. Note that in this more general setting, it is not necessarily true that , because it is also possible that
and
could be incomparable.