## Abstract

Any collection of objects is a
and if
A set is completely determined or defined when
Note that the members are enclosed in brackets and separated by commas. The second method is to state the
where the colon is to be read as ‘such that’.

*set.*The objects are called the*elements*or*members*of the set. It is normal to use upper case letters (i.e. capitals) to denote the sets and lower case letters for the elements of the sets. If an element*p*is a member of a set*A*, we write:$$
p \in A
$$

*p*is not a member we write:$$
p \notin A
$$

*all its members are specified.*This is called the principle of extension. There are two ways in which a particular set can be defined. The first is by specifying its*members*:$$
B = \left\{ {2,4,6} \right\}
$$

*property characterising the elements.*We could therefore express this set*B*equivalently by writing:$$
B = \left\{ {x:x\,is\,a\,positive\,even\,number\,less\,than\,8} \right\}
$$

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## Copyright information

© Jim Dewhurst 1988