# Math Help - Can sets have a repeating element?

1. ## 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?

2. ## 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.