represents the domain of strictly negative real numbers.


  • xNegativeReals evaluates immediately if x is a numeric quantity.
  • Simplify[exprNegativeReals,assum] can be used to try to determine whether an expression corresponds to a negative real number under the given assumptions.
  • (x1|x2|)NegativeReals and {x1,x2,}NegativeReals test whether all xi are negative real numbers.
  • NegativeReals is output in StandardForm and TraditionalForm as . This typeset form can be input using nreals.


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Basic Examples  (3)

is a negative real number:

If is a real number, is a negative real number:

Find negative real solutions of an equation:

Scope  (4)

Test if a numeric quantity is negative:

Make domain membership assumptions:

Specify the default domain over which a function should work:

Test whether several numbers are negative reals:

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

Applications  (1)

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

Properties & Relations  (4)

Membership in NegativeReals is equivalent to membership in Reals along with negativity:

NegativeReals contains NegativeRationals and NegativeIntegers:

NegativeReals is contained in Complexes:

NegativeReals is disjoint from NonNegativeReals and PositiveReals:

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


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


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


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


@misc{reference.wolfram_2024_negativereals, author="Wolfram Research", title="{NegativeReals}", year="2019", howpublished="\url{}", note=[Accessed: 12-July-2024 ]}


@online{reference.wolfram_2024_negativereals, organization={Wolfram Research}, title={NegativeReals}, year={2019}, url={}, note=[Accessed: 12-July-2024 ]}