yields True if is determined to be less than .
yields True if the form a strictly increasing sequence.
- Less gives True or False when its arguments are real numbers.
- Less does some simplification when its arguments are not numbers.
- For exact numeric quantities, Less internally uses numerical approximations to establish numerical ordering. This process can be affected by the setting of the global variable $MaxExtraPrecision.
Examplesopen allclose all
Numeric Inequalities (7)
Symbolic and numeric methods used by Less are insufficient to disprove this inequality:
Use RootReduce to decide the sign of algebraic numbers:
Numeric methods used by Less do not use sufficient precision to prove this inequality:
RootReduce proves the inequality using exact methods:
Increasing $MaxExtraPrecision may also prove the inequality:
Symbolic Inequalities (2)
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)
The negation of three-argument Less does not simplify automatically:
This is not equivalent to three-argument GreaterEqual:
When Less cannot decide inequality between numeric expressions it returns unchanged:
FullSimplify uses exact symbolic transformations to disprove the inequality:
Negative[x] is equivalent to :
Use Reduce to solve inequalities:
Use FindInstance to find solution instances:
Integrate a function over the solution set of inequalities:
Possible Issues (3)
Thanks to automatic precision tracking, Less knows to look only at the first 10 digits:
The extra digits in this case are ignored by Less: