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# Describing a Set

## 1.2 Describing a Set and Function

#### Describing a Set

• It is not always possible to list all the elements in a set (e.g. N, Z, Q, R as above). There is a way of describing sets that is useful for infinite sets (i.e. sets with an infinite number of elements).
• The set of all x such that ____ is denoted as \left\{x:_{-----}\right\}. For example:

i) \{x:0<,\ x<1\} is the set of real numbers strictly between 0 and 1.

ii) \{x:x\leq3\} is the set of real numbers smaller or equal to 3.

iii) \{x: x>0, x \in Q\} is the set of all positive rational numbers.

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