Set Notation and Types of Sets

What is a set?

Think of a set as a labelled basket at the market: the basket for tomatoes only holds tomatoes. A set is a collection of distinct objects, written with curly brackets.

Example: A = {2, 4, 6, 8} means "A is the set containing 2, 4, 6 and 8".

Key notation

• ∈ means "is an element of" - e.g. 4 ∈ A
• ∉ means "is not an element of" - e.g. 5 ∉ A
• n(A) means the number of elements in A - here n(A) = 4
• ∅ or {} is the empty set - a basket with nothing in it
• ξ (xi) is the universal set - every basket sits inside the market itself

Example: If B = {odd numbers less than 10}, then B = {1, 3, 5, 7, 9} and n(B) = 5.

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