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induction-analogy

Generate testable hypotheses from limited observations using induction and analogy.

6|Updated Apr 16, 2026
Search Tags:#discovery#reasoning#induction#hypothesis#cross-domain#analogy#proof
One-click install
npx skills add https://github.com/the-thinker0/math-skill --skill induction-analogy
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: induction-analogy
Source: https://github.com/the-thinker0/math-skill/tree/main/skills/induction-analogy
Command: npx skills add https://github.com/the-thinker0/math-skill --skill induction-analogy

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Induction and analogy are core tools to derive general rules from limited data and to transfer insights across domains, accelerating discovery and cross-field learning.

Core Features & Use Cases

  • Inductive Discovery: generate hypotheses and conjectures from concrete cases;
  • Analogy Transfer: map structural similarities to apply insights across domains;
  • Dual-Mode Support: supports Research mode for formal reasoning and Life mode for practical intuition;
  • Validation Guidance: outlines steps for counterexamples, verification, and, when possible, proofs.

Quick Start

Describe a concrete problem and instruct the AI to apply induction and analogy to generate a testable hypothesis.

Frequently Asked Questions about induction-analogy

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I generate a testable hypothesis from limited observations?▼

Generate testable hypotheses from limited observations by identifying general patterns using mathematical induction, then validating them through structured counterexamples and verification paths. This approach transforms concrete cases into formal conjectures.

What is cross-domain analogy transfer and how does it work?▼

Cross-domain analogy transfer works by mapping structural similarities between distinct fields to apply existing insights to new problems. It accelerates discovery by transferring validated rules from one domain directly into another.

Can I use mathematical induction for proving theorems and cross-domain reasoning?▼

Yes, mathematical induction is explicitly supported for proving theorems and cross-domain reasoning. It operates within a formal Research mode to derive general rules and validate them through structured proof generation.

How to validate inductive hypotheses and find counterexamples?▼

Validate inductive hypotheses by following structured guidance to actively search for counterexamples and execute verification paths. When possible, this validation process advances to formal mathematical proofs to confirm the hypothesis.

Does induction and analogy reasoning apply to learning from experience?▼

Yes, induction and analogy reasoning applies to learning from experience through a dedicated Life mode. This mode uses practical intuition to extract general life rules from concrete events, complementing the formal Research mode.

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