A (data) set is a collection of (data) elements. We can explicitly list the elements in the set or define the set by a property

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The set A consists of the 6 listed elements. The set B consists of apples, pears, bananas, etc.

A data element a belongs to a set A, written a \in A, provided a is a member of the set A. E.g. in the examples above, 3 \in A, but 4 doesn’t belong to A (written 4 \notin A).

The following are common operations on sets:

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We also use the symbol Ø to represent the null set, i.e. the set containing no elements.

Sets obey a number of laws including the following (where S = the universal set containing everything under study):

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An interval is the collection of values between two numbers. If a < b then we can define the following types of intervals:

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The integers are a set consisting of the whole numbers = {…-3,-2 , -1, 0, 1, 2, 3, …}

6 Responses to Sets

  1. Steve Gross says:

    Hi Charles,

    I was confused by the statement above that A = (A∩B) ∪ (A∪B′).

    It seemed to me that it should be A = (A∩B) ∪ (A∩B′).

    Then on the Basic Probability Concepts page I note you do state it as I thought it should be, so I believe it should be changed above.

    • Charles says:

      Yes, you are correct. Thank you very much for catching this typo. I have now corrected the formula on the referenced webpage.
      I appreciate your help in improving the website.

  2. Jonathan Bechtel says:

    Hi Charles,

    Thank you for all this information. I’m wondering…..what does the ‘ mean in A U A’ = S??

    It’s been a long time and it’s not ringing a bell. Thanks.

    • Charles says:

      Hi Jonathan,
      A’ = the complement of A = the set of elements in the sample space S that are not in S. If S = {1,2,3,4,5} and A = {2,4} then A’ = {1,3,5}

  3. Jan says:

    Hello Charles,
    Congratulations with your site.
    A minor typo:
    should be
    In the same way:
    Best regards

    • Charles says:

      Hello Jan,
      Thank you very much for catching this typo. I have just changed the referenced webpage to make the necessary correction.
      I really appreciate your effort to make the website better.

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