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

• 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

• 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