1 + 1 = 3 Proof | Breaking the rules of mathematics

Introduction

This tutorial explores the fascinating concept of how simple errors in mathematical calculations can lead to surprising results, such as 1 + 1 equaling 3 and 2 + 2 equaling 5. The purpose of this guide is to help you understand the importance of adhering to mathematical principles and to highlight the potential for miscalculations. We will also touch on a fun method for multiplying numbers by 11.

Step 1: Understanding 1 + 1 = 3

• Concept Explanation: The statement "1 + 1 = 3" is not mathematically valid, but it shows how a small mistake can lead to incorrect conclusions.
• Example Calculation:
  • Start with the correct equation:

    1 + 1 = 2
    

  • If we make a mistake by misinterpreting the operation, we can mistakenly arrive at 3 through erroneous reasoning.
• Practical Advice: Always double-check your calculations to avoid mistakes that can lead to incorrect results.

Step 2: Discovering the Trick Behind 2 + 2 = 5

• Concept Explanation: The statement "2 + 2 = 5" is a classic example of a mathematical illusion caused by miscalculating.
• Example Calculation:
  • Correct calculation:

    2 + 2 = 4
    

  • Mistaken reasoning may occur if one misapplies the rules of addition.
• Common Pitfalls:
  • Be cautious of assumptions made during calculations.
  • Ensure you are following proper mathematical rules to avoid such errors.

Step 3: Multiplying by 11 Made Easy

• Concept Explanation: Multiplying by 11 can be simplified using a straightforward method.
• Step-by-Step Method:
  1. For a two-digit number (e.g., 34):
     • Separate the digits: 3 and 4.
     • Add the digits together: 3 + 4 = 7.
     • Place the sum between the original digits: 374.
  2. For a three-digit number (e.g., 256):
     • Separate the digits: 2, 5, and 6.
     • Add the middle digit to the outer digits: 2 + 5 = 7 and 5 + 6 = 11.
     • The result is 2816 (carry over the 1).
• Practical Tip: Practice this method with various numbers to become proficient at quickly multiplying by 11.

Conclusion

This tutorial highlights how mathematical errors can lead to unexpected outcomes, emphasizing the importance of accuracy in calculations. By understanding the examples of 1 + 1 = 3 and 2 + 2 = 5, as well as learning a quick method for multiplying by 11, you can enhance your mathematical skills and avoid common pitfalls. Remember, careful attention to detail is key in mathematics!