Mastering the Art of Informal Proof: A Beginner’s Guide
Mathematics is an essential part of our daily lives. Whether we are calculating the tip for a restaurant bill or deciding how much paint to buy for a room, we rely on mathematical principles to make our lives easier. One of the most important concepts in math is proof. A proof is simply a logical argument that demonstrates the truth of a statement. But how can we create a proof that is informal and easy to understand by beginners? In this article, we will provide you with a guide to mastering the art of informal proof.
What is Informal Proof?
Informal proof is a proof that is created using simple language and concepts, without relying on complicated math symbols or equations. Informal proofs are often used to demonstrate the truth of a statement or to help explain a concept in an accessible way. They are particularly useful for beginners who may find traditional formal proofs too complex or confusing.
Creating an Informal Proof: The Basics
To create an informal proof, there are a few things you need to keep in mind. First, it’s important to understand what you are trying to prove. This may involve breaking down the statement into smaller parts or examining different cases. Next, you need to identify the key concepts or principles that are important to your argument. Finally, you need to create a logical argument that demonstrates the truth of the statement using these concepts and principles.
Examples of Informal Proof
Let’s look at some examples of informal proof. Suppose we want to prove that the sum of two even numbers is always even. Here’s a simple informal proof:
“Suppose we have two even numbers, x and y. This means that x = 2a and y = 2b, where a and b are integers. Then, the sum of these two even numbers is x + y = 2a + 2b = 2(a + b), which is clearly even. Therefore, we have demonstrated that the sum of two even numbers is always even.”
Another example involves proving that the product of two negative numbers is always positive:
“Suppose we have two negative numbers, -x and -y. This means that x and y are positive. Then, the product of these two negative numbers is (-x) * (-y) = xy, which is clearly positive. Therefore, we have demonstrated that the product of two negative numbers is always positive.”
Conclusion
In conclusion, informal proof is an essential tool for beginners who are learning the art of proof. By using simple language and concepts, we can create logical arguments that help us understand the truth of a statement. By following the basic steps of creating an informal proof, we can become more proficient at math and improve our problem-solving skills. Happy proofing!
