Does proving c < b from a > c imply a < b?

[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!

 

[S.G. Janssens]

No. Can you find a counterexample?

 

[PeroK]

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!

In other words:

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

There's something not right there.

 

[Physicist97]

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