continuity
Problem-solving strategies for continuity in real analysis
Problem-solving strategies for continuity in real analysis
Problem-solving strategies for proof theory in mathematical logic
Problem-solving strategies for propositional logic in mathematical logic
Problem-solving strategies for convergence in real analysis
Problem-solving strategies for predicate logic in mathematical logic
Problem-solving with Rudin's Real and Complex Analysis textbook
Enter explore mode - a thinking partner for exploring ideas, investigating problems, and clarifying requirements. Use when the user wants to think through something before or during a change.
Challenge system assumptions against accumulated evidence. Triages observations and tensions, detects patterns, generates proposals. The scientific method applied to knowledge systems. Triggers on "/rethink", "review observations", "challenge assumptions", "what have I learned".
Deep concept anatomist that deconstructs any concept through 8 exploration dimensions (history, dialectics, phenomenology, linguistics, formalization, existentialism, aesthetics, meta-philosophy) and compresses insights into an epiphany. Use when user asks to explain, dissect, or deeply understand a concept, term, or idea. Triggers on '解剖概念', '概念解剖', 'explain concept', 'learn concept', '/ljg-learn'. Produces org-mode output.
哈耶克 × 米塞斯 × Claude 三人对话。奥派经济学视角的多角色讨论。 触发方式:/chatroom-austrian、/奥派、「奥派聊天室」 Austrian economics chatroom. Hayek × Mises × Claude debate. Trigger: /chatroom-austrian, /奥派, "Austrian chat"
Act as a collaborative thinking partner for exploring complex problems through questioning, not solutioning. Use when the user wants to think out loud, explore an idea, work through a problem, or asks for a thinking partner.
Force unrelated concepts together to discover emergent properties - "What if we treated X like Y?"
Flip core assumptions to reveal hidden constraints and alternative approaches - "what if the opposite were true?"
Validate AI/ML models and datasets for bias, fairness, and ethical concerns. Use when auditing AI systems for ethical compliance, fairness assessment, or bias detection. Trigger with phrases like "evaluate model fairness", "check for bias", or "validate AI ethics".
Use this when the user wants to deeply understand something through guided questioning. Trigger phrases include: "quiz me", "help me understand", "Socratic", "teach me", "walk me through with questions", "test my understanding", or when the user asks for an explanation and would benefit more from guided discovery than a direct answer.
Ecology, biodiversity, and conservation biology research — species identification, invasive species assessment, pollinator ecology, population dynamics, food webs, trophic interactions, community ecology, island biogeography. Use for ANY ecology question including species distributions, invasive impacts, pollination biology, predator-prey dynamics, or conservation assessment.
Philosophy, decision-making framework, and technical skills for delivering visual, interactive, and educational AI responses.
Use when advising a ruler or superior during a political crisis. Employs historical analogies, proverbs, and consequence analysis to persuade leaders to take difficult but necessary action.
Use when deciding whether to accept honors or rewards. Analyzes the true basis of your position—merit vs. relationship—and evaluates whether accepting creates contradictions that undermine legitimacy.
Use when evaluating whether to wage war against nomadic or mobile enemies. Applies cost-benefit analysis using distance, terrain, force degradation, and the crossbow metaphor (彊弩之极) to recommend diplomacy or engagement.
Use when evaluating whether to enter a powerful party's territory or accept an asymmetric alliance. Applies the earth puppet vs. wooden puppet parable to assess exit options, leverage once inside, and the risk of being trapped with no recourse in a 'tiger and wolf' (虎狼) state.