<P> The etymology of the word is from the Latin aequālis ("equal", "like", "comparable", "similar") from aequus ("equal", "level", "fair", "just"). </P> <P> Leibniz characterized the notion of equality as follows: </P> <Dl> <Dd> Given any x and y, x = y if and only if, given any predicate P, P (x) if and only if P (y). </Dd> </Dl> <Dd> Given any x and y, x = y if and only if, given any predicate P, P (x) if and only if P (y). </Dd>

The relation between two expressions that are not equal