1.2.1

Sets

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Sets of Objects

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Sets

  • Sets are collections of objects.
  • The objects in a set are called its elements.
  • A set is written using curly brackets:
    • {2,3,4} is the set containing 2,3,4
    • {positive even numbers below 5} = {2,4}
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Universal set

  • The symbol ξ is used for the universal set: the set that contains everything.
  • On a Venn diagram, ξ is everything inside the rectangle.
  • The "complement of a set A" is written as A’
    • It is the set of all the things that aren’t in A.
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Empty set

  • The symbol ∅ is used to the empty set: the set that contains no elements.
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Notation

  • If an element e is in a set A, we write:
    • eAe \in A
  • If an element d is not in A, we write:
    • dAd \notin A
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Using rules

  • To define a set A using a rule, we can use the following notation:
    • A=A = {x:x2=4x: x^2 = 4}
    • Where {x:...x:...} means 'all values of xx such that'.
  • This means the set A has the elements {-2, 2}.
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Number of elements

  • The number of elements in a set A is written as n(A).
  • In the example shown here, n({2,3,4}) = 3.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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