x>=y or x≥y
yields True if is determined to be greater than or equal to .
yields True if the form a nonincreasing sequence.
- GreaterEqual is also known as weak inequality or non-strict inequality.
- x≥y can be entered as x >= y or x \[GreaterEqual]y.
- GreaterEqual gives True or False when its arguments are real numbers.
- GreaterEqual does some simplification when its arguments are not numbers.
- For exact numeric quantities, GreaterEqual internally uses numerical approximations to establish numerical ordering. This process can be affected by the setting of the global variable $MaxExtraPrecision.
- In StandardForm, GreaterEqual is printed using ≥.
- x⩾y, entered as x >/ y or x \[GreaterSlantEqual]y, can be used on input as an alternative to x≥y.
Examplesopen allclose all
Numeric Inequalities (7)
Inequalities are defined only for real numbers:
Approximate numbers that differ in at most their last eight binary digits are considered equal:
Compare an exact numeric expression and an approximate number:
Compare two exact numeric expressions; a numeric test may suffice to prove inequality:
Proving this inequality requires symbolic methods:
Symbolic and numeric methods used by GreaterEqual are insufficient to prove this inequality:
Use RootReduce to decide the sign of algebraic numbers:
Numeric methods used by GreaterEqual do not use sufficient precision to disprove this:
RootReduce disproves the inequality using exact methods:
Increasing $MaxExtraPrecision may disprove the inequality:
Symbolic Inequalities (2)
Symbolic inequalities remain unevaluated, since x may not be a real number:
Use Refine to reevaluate the inequality assuming that x is real:
Use Reduce to find an explicit description of the solution set:
Use FindInstance to find a solution instance:
Use Minimize to optimize over the region defined by the inequality:
Use Refine to simplify under assumptions defined by the inequality:
Properties & Relations (12)
The negation of two-argument GreaterEqual is Less:
The negation of three-argument GreaterEqual does not simplify automatically:
Use LogicalExpand to express the negation in terms of two-argument Less:
This is not equivalent to three-argument Less:
When GreaterEqual cannot decide an inequality it returns unchanged:
FullSimplify uses exact symbolic transformations to prove the inequality:
NonNegative[x] is equivalent to :
Use Reduce to solve inequalities:
Use FindInstance to find solution instances:
Use RegionPlot and RegionPlot3D to visualize solution sets of inequalities:
Use Minimize and Maximize to solve optimization problems constrained by inequalities:
Use NMinimize and NMaximize to numerically solve constrained optimization problems:
Integrate a function over the solution set of inequalities:
Use Median, Quantile, and Quartiles to the greatest number(s):
Possible Issues (3)
Inequalities for machine-precision approximate numbers can be subtle:
The result is determined based on extra digits:
Arbitrary-precision approximate numbers do not have this problem:
Thanks to automatic precision tracking, GreaterEqual knows to look only at the first 10 digits:
In this case, inequality between machine numbers gives the expected result:
The extra digits in this case are ignored by GreaterEqual:
Wolfram Research (1988), GreaterEqual, Wolfram Language function, https://reference.wolfram.com/language/ref/GreaterEqual.html (updated 1996).
Wolfram Language. 1988. "GreaterEqual." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/GreaterEqual.html.
Wolfram Language. (1988). GreaterEqual. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GreaterEqual.html