Simplify of -Sqrt[r] >= 0 where r is real

Questions
,
1

Am I missing something? Assuming r is real, the only r that can satisfy -Sqrt[r]>=0 is zero.

$Assumptions = {r \[Element] Reals};
FullSimplify[-Sqrt[r] >= 0]

yields Sqrt[r] <= 0

rather than r==0

2

Either

Reduce[-Sqrt[r] >= 0]

or

Simplify[-Sqrt[r] >= 0, r \[Element] Reals, TransformationFunctions -> {Automatic, Reduce}]

will produce

r == 0

The transformations available to Simplify and FullSimplify are limited to some extent. See the documentation of FullSimplify for a fuller example of using Reduce as a transformation function.

3

Good, I learned something… Thanks.