yields True if is determined to be greater than .
yields True if the form a strictly decreasing sequence.
- Greater gives True or False when its arguments are real numbers.
- Greater does some simplification when its arguments are not numbers.
- For exact numeric quantities, Greater 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 Greater are insufficient to disprove this inequality:
Use RootReduce to decide the sign of algebraic numbers:
Numeric methods used by Greater 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 Greater does not simplify automatically:
This is not equivalent to three-argument LessEqual:
When Greater cannot decide inequality between numeric expressions it returns unchanged:
FullSimplify uses exact symbolic transformations to disprove the inequality:
Positive[x] is equivalent to :
Use Reduce to solve inequalities:
Use FindInstance to find solution instances:
Possible Issues (3)
Thanks to automatic precision tracking, Greater knows to look only at the first 10 digits:
The extra digits in this case are ignored by Greater: