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Properties of Equality

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


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