# Definition: Disjoint Union

**Definition: **Let A and B be sets. The **disjoint union** of A and B is the set, often denoted by , of elements of the form or where and . We thus have, in symbols, .//

The essence of this definition is to give us a way to take the union of sets while still “remembering” where each element came from, i.e., which set it’s from. What this means is that even if the **same** element lies in both A and B, it will still form two **distinct** elements in the disjoint union because we’ve now “labeled” it with the set that it came from (by putting either A or B in the second slot according to which set the element is in originally). This gives us, amongst other things, a perfectly logical way of creating sets that **do** “see duplicates”.

For more on this construction, see lesson 18.

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