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In this part we develop systematically the rules for operations with num-
beers, relations among numbers, and properties of these operations and
relations: addition, multiplication, inequalities, positivity, square roots, n-th
roots. We find many of them, like commutativity and associativity, which
recur frequently in mathematics and apply to other objects. They apply to
complex numbers, but also to functions or mappings (in this case, commute-
trinity does not hold in general and it is always an interesting problem to
determine when it does hold).
Even when we study geometry afterwards, the rules of algebra are still
used, say to compute areas, lengths, etc., which associate numbers with
geometric objects. Thus does algebra mix with geometry
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