LessEqual—Wolfram Documentation
x<=y or x≤y
yields True if x is determined to be less than or equal to y.
x1≤x2≤x3
yields True if the 
form a nondecreasing sequence.
Details
Examples
open all close allScope (9)
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 LessEqual are insufficient to prove this inequality:
Use RootReduce to decide the sign of algebraic numbers:
Numeric methods used by LessEqual do not use sufficient precision to disprove this inequality:
RootReduce disproves the inequality using exact methods:
Increasing $MaxExtraPrecision may also 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 inequality-defined region:
Use Refine to simplify under the inequality-defined assumptions:
Properties & Relations (12)
Possible Issues (3)
Inequalities for machine-precision approximate numbers can be subtle:
The result is based on extra digits:
Arbitrary-precision approximate numbers do not have this problem:
Thanks to automatic precision tracking, LessEqual 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 LessEqual:
History
Introduced in 1988 (1.0) | Updated in 1996 (3.0)
Text
Wolfram Research (1988), LessEqual, Wolfram Language function, https://reference.wolfram.com/language/ref/LessEqual.html (updated 1996).
CMS
Wolfram Language. 1988. "LessEqual." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/LessEqual.html.
APA
Wolfram Language. (1988). LessEqual. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LessEqual.html
BibTeX
@misc{reference.wolfram_2025_lessequal, author="Wolfram Research", title="{LessEqual}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/LessEqual.html}", note=[Accessed: 22-February-2026]}
BibLaTeX
@online{reference.wolfram_2025_lessequal, organization={Wolfram Research}, title={LessEqual}, year={1996}, url={https://reference.wolfram.com/language/ref/LessEqual.html}, note=[Accessed: 22-February-2026]}