{"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-number-system-extension-candidate","title":{"zh-Hant":"自然數、整數、有理數、實數到絕對值候選路徑","en":"From Natural Numbers to Absolute Value on the Real Line"},"summary":{"zh-Hant":"由計數用的自然數進入整數與有理數，以完備化語言建立實數入口，再用絕對值表達數線距離。","en":"Move from natural numbers used for counting to integers and rational numbers, enter the real-number system through completion language, and then express number-line distance with absolute value."},"audience":["general_learner","lower_secondary"],"review":"candidate","nodes":[{"id":"mko-natural-number","position":1,"requirement":"required","rationale":{"zh-Hant":"先建立自然數與零的慣例。","en":"Begin by fixing the convention for natural numbers and zero."}},{"id":"mko-integer","position":2,"requirement":"required","rationale":{"zh-Hant":"加入負方向形成整數。","en":"Add a negative direction to form the integers."}},{"id":"mko-rational-number","position":3,"requirement":"required","rationale":{"zh-Hant":"以兩個整數之比建立有理數，並排除零分母。","en":"Represent rational numbers as ratios of two integers while excluding a zero denominator."}},{"id":"mko-real-number","position":4,"requirement":"required","rationale":{"zh-Hant":"由有理數嵌入與完備化進入實數系。","en":"Enter the real-number system through the rational embedding and completion."}},{"id":"mko-absolute-value","position":5,"requirement":"optional","rationale":{"zh-Hant":"以分段函數表示實數到零的非負距離。","en":"Use a piecewise function to express the nonnegative distance from a real number to zero."}}]},"title":"自然數、整數、有理數、實數到絕對值候選路徑"}