{"schema_version":"ocme-site-results-v1","locale":"zh-Hant","page_type":"paths","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{},"path":{"id":"path-domain-coverage-wave-one","title":{"zh-Hant":"第一波領域覆蓋基礎","en":"Wave-One Domain Foundations"},"summary":{"zh-Hant":"由自然數、集合與命題分支進入算術、方程、機率、歸納、階乘與基本組合計數。","en":"Branch from natural numbers, sets, and propositions into arithmetic, equations, probability, induction, factorials, and elementary combinatorial counting."},"audience":["general_learner","upper_secondary"],"review":"candidate","nodes":[{"id":"mko-natural-number","position":1,"requirement":"required","rationale":{"zh-Hant":"提供算術、歸納與有限計數的自然數基礎。","en":"Supply the natural-number foundation for arithmetic, induction, and finite counting."}},{"id":"mko-set","position":1,"requirement":"required","rationale":{"zh-Hant":"提供樣本空間作為結果集合的基礎。","en":"Supply the set foundation for treating a sample space as a collection of outcomes."}},{"id":"mko-proposition","position":1,"requirement":"required","rationale":{"zh-Hant":"提供歸納法所處理命題族的邏輯基礎。","en":"Supply the logical foundation for proposition families handled by induction."}},{"id":"mko-arithmetic-operations","position":2,"requirement":"required","rationale":{"zh-Hant":"解鎖代數表達與基本計數中的數量組合。","en":"Unlock quantitative combination in algebraic expressions and elementary counting."}},{"id":"mko-sample-space","position":2,"requirement":"optional","rationale":{"zh-Hant":"從集合語言進入機率統計的結果論域。","en":"Move from set language into the outcome domain of probability and statistics."}},{"id":"mko-mathematical-induction","position":2,"requirement":"optional","rationale":{"zh-Hant":"從自然數與命題進入結構化證明方法。","en":"Move from natural numbers and propositions into a structured proof method."}},{"id":"mko-variable-expression","position":3,"requirement":"optional","rationale":{"zh-Hant":"從算術運算進入含變數的代數表達。","en":"Move from arithmetic operations into algebraic expressions containing variables."}},{"id":"mko-counting-principle","position":3,"requirement":"optional","rationale":{"zh-Hant":"以自然數與算術運算組合有限選擇數量。","en":"Combine counts of finite choices using natural numbers and arithmetic operations."}},{"id":"mko-factorial","position":3,"requirement":"optional","rationale":{"zh-Hant":"以自然數乘法與後繼遞迴建立有限乘積。","en":"Use natural-number multiplication and successor recursion to build a finite product."}},{"id":"mko-equation","position":4,"requirement":"optional","rationale":{"zh-Hant":"由表達式進入等式、解集與代入驗證。","en":"Move from expressions into equality, solution sets, and substitution checks."}},{"id":"mko-linear-equation","position":5,"requirement":"optional","rationale":{"zh-Hant":"以非零一次係數收斂到唯一解與退化分類。","en":"Use a nonzero linear coefficient to obtain a unique solution and distinguish the degenerate constant cases."}}]},"title":"第一波領域覆蓋基礎"}