Geometry with Trigonometry

Sec. 1.6 Pre-requisites 19

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B C

D

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Figure 1.22. A parallelogram.

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B C

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A rectangle.

1.6 Pre-requisites

Although this book re-starts geometry and trigonometry from the beginning, it does
not take mathematics from a start. Consequently there is material from other parts of
mathematics which is assumed known. This also should be revised at the start, or at
the appropriate time when it is needed.
At the beginning, we presuppose a moderate knowledge of set theory, sufficient
to deal with sets, relations and functions, in particular order and equivalence rela-
tions. From Chapter 3 on we assume a knowledge of the real number system, and the
elementary algebra involved. Later requirements come in gradually.

1.6.1 Setnotation

For set notation we refer to Smith [12, pages 1 – 38]. We mention that we use the
wordfunctionwhere it usesmap. We should also like to emphasise the difference
between a set{a,b}and a couple or ordered pair(a,b). In a set, the order of the
elements does not matter, so that{a,b}={b,a}in all cases, and

{a,b}={c,d}

if and only if either

a=c and b=d

or

a=d and b=c.

In a couple(a,b)it matters which is first and which is second. Thus(a,b)=(b,a)
unlessa=b,and

(a,b)=(c,d)

if and only if

a=c and b=d.