A conditional equation is an equation that is true for at least one, but not every, value of its variables
in a specified domain. Its solution
set is therefore a nonempty proper
subset of the domain. For example, over the real
numbers, 
is conditional because it is true only for 
.
An equation that is true for every value in its domain is an identity. An equation with no solutions in its domain is an inconsistent equation rather than a conditional equation.
