NegativeRationals
represents the domain of strictly negative rational numbers, as in x∈NegativeRationals.
Details
- x∈NegativeRationals evaluates immediately if x is a numeric quantity.
- Simplify[expr∈NegativeRationals,assum] can be used to try to determine whether an expression corresponds to a negative rational number under the given assumptions.
- (x1x2…)∈NegativeRationals and {x1,x2,…}∈NegativeRationals test whether all xi are negative rational numbers.
- The domain of negative integers is taken to be a subset of the domain of negative rationals.
- NegativeRationals is output in StandardForm or TraditionalForm as
![TemplateBox[{}, NegativeRationals]](Files/NegativeRationals.en/1.png "TemplateBox[{}, NegativeRationals]")
. This typeset form can be input using 
nrats
.
Examples
open all close allBasic Examples (3)
Scope (5)
Test domain membership of a numeric expression:
Make domain membership assumptions:
Specify the default domain over which Reduce should work:
Test whether several numbers are negative rationals:
If any number is explicitly not a negative rational, the result is False:
TraditionalForm formatting:
Properties & Relations (4)
Membership in NegativeRationals is equivalent to membership in Rationals and negativity:
NegativeRationals contains NegativeIntegers:
NegativeRationals is contained in NegativeReals, Algebraics and Complexes:
NegativeRationals is disjoint from NonNegativeRationals and PositiveRationals:
Text
Wolfram Research (2019), NegativeRationals, Wolfram Language function, https://reference.wolfram.com/language/ref/NegativeRationals.html.
CMS
Wolfram Language. 2019. "NegativeRationals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NegativeRationals.html.
APA
Wolfram Language. (2019). NegativeRationals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NegativeRationals.html