NonNegativeReals
represents the domain of non-negative real numbers.
Details
- x∈NonNegativeReals evaluates immediately if x is a numeric quantity.
- Simplify[expr∈NonNegativeReals,assum] can be used to try to determine whether an expression corresponds to a non-negative real number under the given assumptions.
- (x1x2…)∈NonNegativeReals and {x1,x2,…}∈NonNegativeReals test whether all xi are non-negative real numbers.
- NonNegativeReals is output in StandardForm and TraditionalForm as
. This typeset form can be input using 
nnreals
.
Examples
open all close allBasic Examples (3)
is a non-negative real number:
Element[Pi ^ E, NonNegativeReals]If 
is a real number, then 
is a non-negative real number:
Simplify[Sin[x] + 1∈NonNegativeReals, x∈ℝ]Find non-negative real solutions of an equation:
Reduce[x ^ 5 - 2x + 1 == 0, x, NonNegativeReals]Scope (4)
Test if a numeric quantity is non-negative:
Sin[5]∈NonNegativeRealsMake domain membership assumptions:
Refine[Sign[Im[x + I y]], (x | y)∈NonNegativeReals]Integrate[Abs[1 - Abs[x + 2]], x, Assumptions -> x∈NonNegativeReals]Specify the default domain over which a function should work:
Reduce[E ^ x - 2x == 3, x, NonNegativeReals]Resolve[Exists[x, y == Sqrt[x]], NonNegativeReals]Test whether several numbers are non-negative reals:
(x | y | 1)∈NonNegativeRealsIf any number is explicitly not a non-negative number, the result is False:
{x, y, -1}∈NonNegativeRealsApplications (1)
Properties & Relations (4)
Membership in NonNegativeReals is equivalent to membership in Reals along with non-negativity:
x∈NonNegativeRealsNonNegativeReals contains NonNegativeRationals and NonNegativeIntegers:
Refine[x∈NonNegativeReals, x∈NonNegativeRationals]Refine[x∈NonNegativeReals, x∈NonNegativeIntegers]NonNegativeReals is contained in Complexes:
Refine[x∈ℂ, x∈NonNegativeReals]NonNegativeReals is disjoint from NegativeReals:
Reduce[x∈NegativeReals, x, NonNegativeReals]It intersects NonPositiveReals:
Reduce[x∈NonPositiveReals, x, NonNegativeReals]Text
Wolfram Research (2019), NonNegativeReals, Wolfram Language function, https://reference.wolfram.com/language/ref/NonNegativeReals.html.
CMS
Wolfram Language. 2019. "NonNegativeReals." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NonNegativeReals.html.
APA
Wolfram Language. (2019). NonNegativeReals. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NonNegativeReals.html