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Math Help - Can sets have a repeating element?

  1. #1
    Member Jskid's Avatar
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    Can sets have a repeating element?

    Can a set have an element that repeats, for example {1,2,2,3}?
    According to wikipedia "A set is a collection of distinct objects, considered as an object in its own right" so I guess not; however would it be different if it was not a set of numbers, for example if you had a set of boxes and two happened to be the same?
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  2. #2
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    Re: Can sets have a repeating element?

    In a set, the number of times an element (whether a number or a box) occurs does not matter. We have {1, 2, 2, 3} = {1, 2, 3}. In fact, the axiom of extensionality says that A = B as sets iff x\in A\Leftrightarrow x\in B for all x. Now, the proposition x\in A does not count the number of times x occurs in A; x either occurs or it does not.

    In contrast, in multisets the number of times an element occurs (multiplicity) matters.
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