represents the domain of strictly negative integers, as in xNegativeIntegers.


  • xNegativeIntegers evaluates immediately if x is a numeric quantity.
  • Simplify[exprNegativeIntegers,assum] can be used to try to determine whether an expression is a negative integer under the given assumptions.
  • (x1|x2|)NegativeIntegers and {x1,x2,}NegativeIntegers test whether all xi are negative integers.
  • NegativeIntegers is output in StandardForm or TraditionalForm as TemplateBox[{}, NegativeIntegers]. This typeset form can be input using nints.


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Basic Examples  (3)

Minus seven is a negative integer:

If is an integer, is a negative integer:

Find negative integer solutions of a Pell equation:

Scope  (6)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain over which a function should work:

Solve an optimization problem over the negative integers:

Test whether several numbers are negative integers:

If any number is explicitly not a negative integer, the result is False:

TraditionalForm formatting:

Applications  (1)

Testing membership in the negative integers is a fast way to verify negativity of a large list of integers:

Properties & Relations  (3)

Membership in NegativeIntegers is equivalent to membership in Integers along with negativity:

NegativeIntegers is contained in NegativeReals and NegativeRationals:

NegativeIntegers is disjoint from NonPositiveIntegers and PositiveIntegers:

Wolfram Research (2019), NegativeIntegers, Wolfram Language function,


Wolfram Research (2019), NegativeIntegers, Wolfram Language function,


Wolfram Language. 2019. "NegativeIntegers." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2019). NegativeIntegers. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_negativeintegers, author="Wolfram Research", title="{NegativeIntegers}", year="2019", howpublished="\url{}", note=[Accessed: 20-June-2024 ]}


@online{reference.wolfram_2024_negativeintegers, organization={Wolfram Research}, title={NegativeIntegers}, year={2019}, url={}, note=[Accessed: 20-June-2024 ]}