Inequalities

Inequality tester

Hunt for counterexamples. Testing is not proving.

For checking your work after you’ve tried it yourself.

Step 1:
Type the inequality

Like (a+b)/2 >= sqrt(ab).

Step 2:
Set the variables

Positive, any real, whole numbers or a range, plus any conditions.

Step 3:
Run the test

Read where it's tightest, then Do it by hand.
What it does.
Tries your inequality at many points: special ones first (all equal, one tiny, one huge), then random ones. It reports any counterexample, the point where it comes closest to failing, and where equality seems to hold.
When it helps.
Checking an inequality before you try to prove it, or finding where equality happens.
What it won’t do.
Testing is not proving. Passing every test is evidence, not a proof.
Example.
a+b2≥ab\frac{a+b}{2} \ge \sqrt{ab} passes, with equality when a=ba = b.
An inequality in a, b, c, d, x, y or z
Trials

Use >=, <=, >, < or =. Each run uses a fresh random seed.

Try

Testing is not proving. Passing every test is evidence, not a proof.