WOLFRAM

represents the domain of strictly negative real numbers.

Details

  • 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.

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

is a negative real number:

Out[1]=1

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

Out[1]=1

Find negative real solutions of an equation:

Out[1]=1

Scope  (4)Survey of the scope of standard use cases

Test if a numeric quantity is negative:

Out[1]=1

Make domain membership assumptions:

Out[1]=1
Out[2]=2

Specify the default domain over which a function should work:

Out[1]=1
Out[2]=2

Test whether several numbers are negative reals:

Out[1]=1

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

Out[2]=2

Applications  (1)Sample problems that can be solved with this function

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

Out[2]=2
Out[3]=3

Properties & Relations  (4)Properties of the function, and connections to other functions

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

Out[1]=1

NegativeReals contains NegativeRationals and NegativeIntegers:

Out[1]=1
Out[2]=2

NegativeReals is contained in Complexes:

Out[1]=1

NegativeReals is disjoint from NonNegativeReals and PositiveReals:

Out[1]=1
Out[2]=2
Wolfram Research (2019), NegativeReals, Wolfram Language function, https://reference.wolfram.com/language/ref/NegativeReals.html.
Wolfram Research (2019), NegativeReals, Wolfram Language function, https://reference.wolfram.com/language/ref/NegativeReals.html.

Text

Wolfram Research (2019), NegativeReals, Wolfram Language function, https://reference.wolfram.com/language/ref/NegativeReals.html.

Wolfram Research (2019), NegativeReals, Wolfram Language function, https://reference.wolfram.com/language/ref/NegativeReals.html.

CMS

Wolfram Language. 2019. "NegativeReals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NegativeReals.html.

Wolfram Language. 2019. "NegativeReals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NegativeReals.html.

APA

Wolfram Language. (2019). NegativeReals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NegativeReals.html

Wolfram Language. (2019). NegativeReals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NegativeReals.html

BibTeX

@misc{reference.wolfram_2025_negativereals, author="Wolfram Research", title="{NegativeReals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NegativeReals.html}", note=[Accessed: 18-February-2025 ]}

@misc{reference.wolfram_2025_negativereals, author="Wolfram Research", title="{NegativeReals}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/NegativeReals.html}", note=[Accessed: 18-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_negativereals, organization={Wolfram Research}, title={NegativeReals}, year={2019}, url={https://reference.wolfram.com/language/ref/NegativeReals.html}, note=[Accessed: 18-February-2025 ]}

@online{reference.wolfram_2025_negativereals, organization={Wolfram Research}, title={NegativeReals}, year={2019}, url={https://reference.wolfram.com/language/ref/NegativeReals.html}, note=[Accessed: 18-February-2025 ]}