Union
Details and Options
- If the listi are considered as sets, Union gives their union.
- Union [list1,list2,…] can be input in StandardForm and InputForm as list1⋃list2⋃…. The character ⋃ can be entered as un or \[Union] .
- The listi must have the same head, but it need not be List .
- Union [list1,…,SameTest->test] applies test to each pair of elements in the listi to determine whether they should be considered the same.
Examples
open all close allBasic Examples (3)
Give a sorted list of distinct elements:
Give a sorted list of distinct elements from all the lists:
Enter using un:
Scope (1)
Give a list of the distinct lists:
Options (4)
Applications (4)
Find divisors that occur in any of 10, 12, and 20:
Find all the triples of bits that occur in the binary decomposition of 10!:
Find the distinct elements in the iteration:
Find what options are used by a list of functions:
Properties & Relations (3)
Split on the sorted set gives lists of the same elements:
The union is equivalent to the first elements of these lists:
Tally gets the count of identical elements and returns them in the original order:
The union is the sorted list of the elements returned by Tally :
DeleteDuplicates is similar to Union without sorting:
Avoiding the sort improves the speed substantially:
See Also
Join Intersection Complement SymmetricDifference Tally DeleteDuplicates BinLists Split Or BitOr
Characters: \[Union]
Function Repository: MultisetUnion MultisetSum
Tech Notes
Related Guides
-
▪
- Rearranging & Restructuring Lists ▪
- Operations on Sets ▪
- Discrete & Integer Data ▪
- Math & Counting Operations on Lists ▪
- Database-Like Operations on Datasets ▪
- Finite Mathematics ▪
- Handling Arrays of Data ▪
- Discrete Mathematics ▪
- Tabular Transformation ▪
- Computation with Structured Datasets ▪
- Numerical Data
History
Introduced in 1988 (1.0) | Updated in 1996 (3.0)
Text
Wolfram Research (1988), Union, Wolfram Language function, https://reference.wolfram.com/language/ref/Union.html (updated 1996).
CMS
Wolfram Language. 1988. "Union." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Union.html.
APA
Wolfram Language. (1988). Union. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Union.html
BibTeX
@misc{reference.wolfram_2025_union, author="Wolfram Research", title="{Union}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Union.html}", note=[Accessed: 05-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_union, organization={Wolfram Research}, title={Union}, year={1996}, url={https://reference.wolfram.com/language/ref/Union.html}, note=[Accessed: 05-December-2025]}