### instructions for answer formulation

use this framework to answer any [question]:

Step 1: Identify Fundamental Components

Break Down the Subject into Basic Elements Example: In chemistry, when explaining why salt dissolves in water:
Components: Salt (sodium chloride), water molecules, ionic bonds, and hydrogen bonds.

Step 2: Understand Interactions and Dynamics

Examine How Components Interact and Change Over Time Example: The polar water molecules interact with the positive (Na⁺) and negative (Cl⁻) ions in salt, pulling them apart and causing the salt to dissolve.

Step 3: Apply Relevant Principles and Theories

Use Foundational Concepts Pertinent to the Field Example: Apply the principles of solvation and intermolecular forces, recognizing that "like dissolves like"—polar solvents dissolve polar or ionic compounds.

Step 4: Establish Cause-and-Effect Relationships

Determine How Interactions Lead to Outcomes Example: The attraction between water molecules and salt ions overcomes the ionic bonds in salt, resulting in dissolution.

Step 5: Synthesize and Communicate Coherently

Integrate Insights into a Clear Explanation Example: Summarize that salt dissolves in water because water molecules surround and separate the salt ions due to electrical attractions, leading to a homogeneous solution.

Applying the Model Step-by-Step with Examples

Step 1: Deconstruction

Break Down the Question to Understand What Is Being Asked Example: For the question, "Why do leaves change color in autumn?"
Components: Leaves, chlorophyll, other pigments (carotenoids and anthocyanins), sunlight, temperature.

Step 2: Exploration

Investigate How the Elements Function Independently and Together Example: Chlorophyll gives leaves their green color and is used in photosynthesis. Other pigments are present but masked by chlorophyll during the growing season.

Step 3: Theoretical Application

Bring in Established Knowledge or Theories Example: Understand that shorter days and cooler temperatures in autumn reduce chlorophyll production, allowing other pigments to become visible.

Step 4: Causal Linking

Connect Cause and Effect to Explain Outcomes Example: The decrease in chlorophyll causes the green color to fade, revealing yellows and oranges from carotenoids and reds from anthocyanins.

Step 5: Explanation Formation

Assemble Insights into a Comprehensive Answer Example: Leaves change color in autumn because reduced sunlight and cooler temperatures halt chlorophyll production, unveiling other pigments that were previously hidden.

### instructions for formulating example

to formulate a strong example that effectively illustrates a given concept, please follow this chain-of-thought:

1. Understand the Concept:
	- Clearly define the concept you aim to illustrate.
	- Ensure your understanding aligns with established definitions and principles.
1. Identify Key Features:
	- List the critical aspects and functions of the concept.
	- Determine what makes this concept unique or important.
2. Consider the Audience:
	- Determine the knowledge level and background of the intended audience.
	- Use language and terminology appropriate for their understanding.
3. Establish Relevance:
	- Ensure the example is directly related to the concept without introducing irrelevant information.
	- Maintain consistency with the subject matter.
4. Create a Real-World Scenario:
	- Ground the example in a practical, real-life situation.
	- Incorporate contexts that are culturally or socially relevant to the audience.
5. Ensure Clarity and Simplicity:
	- Present the example using clear and concise language.
	- Avoid unnecessary complexity to keep the focus on the main idea.
6. Enhance Engagement:
	- Craft the scenario to be interesting and relatable.
	- Stimulate curiosity or emotional connection to make it memorable.
7. Demonstrate the Concept in Action:
	- Show how the concept functions within the scenario.
	- Highlight cause-and-effect relationships and critical features.
8. Promote Inclusivity and Variety:
	- Avoid stereotypes and biases.
	- Consider diverse perspectives and examples that are inclusive.
9. Adjust Complexity Appropriately:
	- Match the complexity of the example to the learner's level.
	- Start with simple elements and build up if necessary.
10. Encourage Critical Thinking:
	- Include open-ended questions or prompts within the example.
	- Encourage the learner to apply the concept to solve a problem.
11. Enhance Memorability:
	- Use analogies or metaphors related to the learner's experiences.
	- Consider framing the example within a compelling story.
12. Verify Accuracy and Correctness:
	- Ensure all information is factual and free from errors.
	- Maintain logical consistency throughout the example.
13. Review and Refine:
	- Read through the example to check for clarity and coherence.
	- Make adjustments to improve engagement and understanding.
14. Final Task:
	- Present the fully developed example in a clear and engaging manner.
	- Ensure it stands alone and is understandable without requiring additional context.
	- Aim to not only explain the concept but also to resonate with the learner, making the learning process both effective and enjoyable.

[question] = what is inequality in mathematics?