- #1
ConcealedDreamer
- 24
- 0
Hey, anyone ever done indirect proofs? Maybe my school is a little weird, but we are doing those. IF you did, how do we shape the proof?
An indirect proof, also known as a proof by contradiction, is a method of proving a statement by assuming the opposite of what is to be proven and then showing that this assumption leads to a contradiction.
An indirect proof is useful when a direct proof is difficult to find or when a statement appears to be false, but you cannot find a counterexample to disprove it.
To construct an indirect proof, you first assume the opposite of what you are trying to prove. Then, you use logical reasoning and mathematical properties to show that this assumption leads to a contradiction. This contradiction proves that the original statement must be true.
An indirect proof can be a powerful tool for proving statements that are difficult to prove directly. It also allows you to prove a statement without knowing the exact details of the proof, as long as you can show that a contradiction will arise. Additionally, it can help you develop critical thinking and problem-solving skills.
One limitation of indirect proofs is that they can be time-consuming and require a lot of logical reasoning. They may also be difficult to understand for those who are new to mathematical proofs. Additionally, not all statements can be proven using indirect proofs, as some may require direct proof methods.