{"schema_version":"ocme-site-results-v1","locale":"en","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":{"from":"/en/paths/"},"path":{"id":"path-foundational-language-candidate","title":{"zh-Hant":"數學基礎語言候選路徑","en":"Foundational Mathematical Language"},"summary":{"zh-Hant":"從計數的具體語言前進到集合、命題與邏輯連接詞，建立閱讀後續數學物件所需的基礎語言。","en":"Move from the concrete language of counting to sets, propositions, and logical connectives, establishing the vocabulary needed to read later mathematical objects."},"audience":["general_learner","upper_secondary"],"review":"candidate","nodes":[{"id":"mko-natural-number","position":1,"requirement":"required","rationale":{"zh-Hant":"先用熟悉的計數對象建立數學概念與符號的區分。","en":"Begin with familiar counting objects to distinguish mathematical concepts from their symbols."}},{"id":"mko-set","position":2,"requirement":"required","rationale":{"zh-Hant":"再以集合整理對象、元素與整體之間的語言。","en":"Use sets to organize objects and the relation between elements and wholes."}},{"id":"mko-proposition","position":3,"requirement":"required","rationale":{"zh-Hant":"引入可被斷言、判定與證明的數學陳述。","en":"Introduce mathematical statements that can be asserted, evaluated, and proved."}},{"id":"mko-logical-connectives","position":4,"requirement":"required","rationale":{"zh-Hant":"用否定、合取、析取、蘊涵與雙條件組合命題。","en":"Use logical connectives—negation, conjunction, disjunction, implication, and biconditional—to combine propositions."}},{"id":"mko-proof","position":5,"requirement":"required","rationale":{"zh-Hant":"以明示前提與合法推理建立結論。","en":"Use explicit premises and valid inference steps to establish a conclusion."}}]},"title":"Foundational Mathematical Language"}