In economics, especially in theoretical economics, it is often necessary to formally prove your statements. Meaning to show your statements are correct in a logical way. One possible way of showing that your statements are correct is by providing an indirect proof. The following couple of lines try to explain the concept of indirect proof in a simple way.
Let’s say you want to indirectly prove , i.e. follows . In order to do so, the first step is to assume that is false. The second step is to show that you end up in a logical contradiction because of your assumption that is false.
The way you formally express this is by adding to your initial condition and to show that leads to a contradiction. In order to show that leads to a contradiction you have to show one of the following three statements:
(Where is an obvious false statement)
If you are able to show one of the above you can conclude that is false. This means that if is correct has to be wrong. Knowing that is false, lets us conclude that is true. Consequently we know that , i.e. we have indirectly proven that the statement is true. Even though this seems confusing at the beginning it is based on pure logic and often used.