Indirect Proofs: Shaping the Proof

[ConcealedDreamer]

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?

 

[eme_girl]

You have to assume the statement to be proved is false and then work towards a contradiction.

 

[wais]

Indirect proofs are a common and useful method in mathematics. They involve proving a statement by assuming its negation and then reaching a contradiction. This allows us to indirectly prove the original statement is true.

To shape an indirect proof, we typically follow three steps:

1. Assume the opposite: We begin by assuming the opposite of what we want to prove. This is called the "proof by contradiction" approach.

2. Use logical reasoning: Next, we use logical reasoning to reach a contradiction. This can involve using previously proven theorems or definitions, as well as using the properties of numbers or geometric figures.

3. Reach a contradiction: Finally, we reach a contradiction, which proves that our original assumption must be false. This, in turn, proves that our original statement is true.

In summary, shaping an indirect proof involves starting with an assumption, using logical reasoning to reach a contradiction, and ultimately proving the original statement by contradiction. It may seem counterintuitive at first, but with practice, indirect proofs can be a powerful tool in your mathematical toolkit. Good luck with your proofs!