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NonNegativeReals

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.
(x₁|x₂|…)∈NonNegativeReals and {x₁,x₂,…}∈NonNegativeReals test whether all x_i are non-negative real numbers.
NonNegativeReals is output in StandardForm and TraditionalForm as . This typeset form can be input using nnreals.

Examples

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Basic Examples (3)

is a non-negative real number:

If is a real number, then is a non-negative real number:

Find non-negative real solutions of an equation:

Scope (4)

Test if a numeric quantity is non-negative:

Make domain membership assumptions:

Specify the default domain over which a function should work:

Test whether several numbers are non-negative reals:

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

Applications (1)

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

Properties & Relations (4)

Membership in NonNegativeReals is equivalent to membership in Reals along with non-negativity:

NonNegativeReals contains NonNegativeRationals and NonNegativeIntegers:

NonNegativeReals is contained in Complexes:

NonNegativeReals is disjoint from NegativeReals:

It intersects NonPositiveReals:

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