Problem: You asked for a thorough, detailed explanation to understand a topic without missing anything. 1. Clarify the goal and scope. Tell me the exact topic, what you already know, and what level of detail you want. 2. Definitions and notation. I will give precise definitions in plain language and then provide formal notation or symbols if needed, using $...$ for any inline math. 3. Step-by-step derivation. I will show each algebraic or logical step, include intermediate results, and explain why each step is valid. 4. Worked examples. I will provide a complete worked example that follows the method, with checks and comments at each stage. 5. Intuition and interpretation. I will explain the intuition behind steps and the meaning of results to build conceptual understanding. 6. Common pitfalls and checks. I will point out typical mistakes, how to avoid them, and quick checks you can use to verify your work. 7. Practice and variation. I will offer practice problems of increasing difficulty and can provide full solutions on request. 8. How to proceed now. Please tell me the specific topic or paste the exact problem you want explained, including any attempts you made and what you find confusing, and I will produce a complete, no-omission explanation following the structure above.