Basic Proofs
A proof is like building a path step by step to show why something is true.
Brief Introduction
Think of a proof as being a detective who needs to solve a puzzle 🔍. Just like detectives use clues and evidence to reach a conclusion, mathematicians use proofs to show why mathematical statements are true. We start with facts we know are true and use logical steps to reach our final answer.
Main Explanation
Starting Point 📌
Every proof begins with something we know is true (like given facts or definitions). It's like starting a journey with a map and knowing your starting location.
Logical Steps ➡️
Each step in a proof must follow logically from previous steps. It's like building a bridge - each piece must connect firmly to the previous one.
Clear Reasoning 💭
We must explain why each step is true, just like explaining to a friend why you chose a particular route to get somewhere.
Conclusion 🎯
The proof ends when we reach our target statement. Like completing a puzzle, all pieces must fit together to show the final picture.
Examples
- Proving why all squares have four equal sides is like showing someone how to make a perfect sandwich - you start with the definition of a square, then explain step by step why each side must be equal.
- If you want to prove why 2 + 2 = 4, it's like explaining to a child why two pairs of shoes make four shoes - you can physically show them and count.
- Proving that all right angles are 90 degrees is like showing why a door needs to open at exactly that angle to stand straight - you can demonstrate it with real objects and measurements.