Prove inequalities by chaining classical bounds like AM-GM and Cauchy-Schwarz.
npx skills add https://github.com/0bserver07/bourbaki --skill inequality-chain
Please help me install this Agent Skill. Skill: inequality-chain Source: https://github.com/0bserver07/bourbaki/tree/main/src/skills/inequality-chain Command: npx skills add https://github.com/0bserver07/bourbaki --skill inequality-chain
Prove inequalities by combining classical inequalities and chaining bounds in analysis, providing a structured workflow for verifying bounds and deriving results.
To get started, provide a concrete inequality problem and I will apply AM-GM, Cauchy–Schwarz, and chaining to derive a bound.
High-intent search queries and answers about installing and using this skill.
You prove inequalities by classifying expressions, selecting classical patterns like AM-GM or Cauchy-Schwarz, and chaining bounds to derive verifiable results. Provide a concrete problem to trigger this structured workflow.
Inequality chaining is a proof strategy combining classical inequalities to bound sums, products, and absolute values. It provides a step-by-step framework for deriving tight estimates in analysis and norm-based problems.
Yes, you can formalize inequality proofs in Lean. The method provides optional formalization guidance and ready-to-use templates to verify bounds derived from AM-GM, Cauchy-Schwarz, and Jensen's inequality.
Use triangle inequality and Jensen's inequality when bounding expressions involving absolute values, norms, or convex functions. These classical tools are essential for deriving tight estimates in optimization and real analysis.
The best way to chain inequalities is following a systematic method: classify the problem, select appropriate classical patterns, and apply chaining sequentially. This structured approach ensures bounds remain tight and verifiable.
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