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Algebra
> Properties of Equality
Properties of Equality
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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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