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Complement[eall,e1,e2,…]

gives the elements in eall that are not in any of the ei.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Generalizations & Extensions  
Options  
SameTest  
Applications  
Properties & Relations  
See Also
Tech Notes
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Complement

Complement[eall,e1,e2,…]

gives the elements in eall that are not in any of the ei.

Details and Options

  • The list returned by Complement is sorted into standard order.
  • Complement[eall,e1,…,SameTest->test] applies test to each pair of elements in eall and the ei to determine whether they should be considered the same.

Examples

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Basic Examples  (1)

Find which elements in the first list are not in any of the subsequent lists:

Generalizations & Extensions  (1)

Complement works with any head, not just List:

Options  (3)

SameTest  (3)

Use equivalence classes based on absolute value:

Use equivalence classes based on Floor:

Use Total of list elements:

Applications  (4)

Find divisors of 20 that are not also divisors of 12:

Find which triples of digits do not occur in the binary decomposition of 12345:

Find which options to Plot are not also options to Graphics:

Find which length-5 sequences never occur after 2 steps in any elementary cellular automaton:

Properties & Relations  (1)

The result of Complement[list1,list2] is sorted and does not contain repeated elements:

This returns the same elements, but preserving the original order and multiplicity in list1:

Use DeleteDuplicates to preserve order but remove multiplicity:

Wolfram Research (1988), Complement, Wolfram Language function, https://reference.wolfram.com/language/ref/Complement.html (updated 1996).

Text

Wolfram Research (1988), Complement, Wolfram Language function, https://reference.wolfram.com/language/ref/Complement.html (updated 1996).

CMS

Wolfram Language. 1988. "Complement." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Complement.html.

APA

Wolfram Language. (1988). Complement. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Complement.html

BibTeX

@misc{reference.wolfram_2025_complement, author="Wolfram Research", title="{Complement}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Complement.html}", note=[Accessed: 30-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_complement, organization={Wolfram Research}, title={Complement}, year={1996}, url={https://reference.wolfram.com/language/ref/Complement.html}, note=[Accessed: 30-August-2025]}