. For , define to mean: then means that f induces a well-defined function of the quotients . Thus, the PER captures both the idea of definedness on the quotients and of two functions inducing the same function on the quotient. Equality of IEEE floating point values The IEEE 754:2008 floating point standard defines an "EQ" relation for floating point values. This predicate is symmetrical and transitive, but is not reflexive because of the presence of NaN values that are not EQ to themselves. Notes References Symmetric relations Transitive relations Equivalence (mathematics)