NegativeReals

represents the domain of strictly negative real numbers.

Details

x∈NegativeReals evaluates immediately if x is a numeric quantity.
Simplify[expr∈NegativeReals,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 x_i are negative real numbers.
NegativeReals is output in StandardForm and TraditionalForm as . This typeset form can be input using nreals.

Examples

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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:

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