# Is this statement for proving inequalities true?

1. Feb 7, 2016

### Physicist97

Hello! What I'm wondering is if you want to prove an inequality, let's say $a<b$ and you already know that $a>c$ is true. If you are able to prove that $c<b$ is true, would that go on to imply that $a<b$ is true also? If this is correct, is it known as a theorem?

Thank you!

2. Feb 7, 2016

### Krylov

No. Can you find a counterexample?

3. Feb 7, 2016

### PeroK

In other words:

$c < a$ and $c < b$ implies $a < b$

There's something not right there.

4. Feb 7, 2016

### Physicist97

Mhmm, yea I see where I went wrong haha. It was a pretty silly mistake, too :). Thank you everyone.