The relation of equality

* Reflexive: a = a

* Symmetric: if a = b then b = a

* Transitive: if a = b and b = c then a = c

Laws of equality

The relation of equality:

* If a = b and c = d then we have a + c = b + d and ac = bd

* If a = b then we have a + c = b + c

Laws of inequality

The relation of inequality:

* If a < b and b < c then we have a < c

* If a < b and c < d then we have a + c < b + d

* If a < b and c > 0 then we have ac < bc

* If a < b and c < 0 then we have bc < ac