{"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-pulse-foundations-20261003","title":{"zh-Hant":"七輪代數與機率基礎：冪、恆等式、函數與有限模型","en":"Seven-Round Algebra and Probability Foundations: Powers, Identities, Functions, and Finite Models"},"summary":{"zh-Hant":"在既有數系與函數基礎上依相依順序完成七個可追溯知識物件。","en":"Complete seven traceable knowledge objects in dependency order on top of the existing number-system and function foundations."},"audience":["general_learner","upper_secondary"],"review":"candidate","nodes":[{"id":"mko-arithmetic-operations","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-real-number","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-variable-expression","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-rational-number","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-equation","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-function-mapping","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-linear-equation","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-coordinate-plane","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-event","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-ratio-proportion","position":1,"requirement":"required","rationale":{"zh-Hant":"本脈衝新物件的既有 Canonical 前置。","en":"Existing canonical prerequisite for the new objects in this pulse."}},{"id":"mko-power-root","position":2,"requirement":"optional","rationale":{"zh-Hant":"本輪限定實數底數的自然數冪，以及非負實數的主平方根，分開冪運算、根值與解集。","en":"This entry covers natural-number powers of real bases and principal square roots of nonnegative real numbers, keeping powers, root values, and solution sets distinct."}},{"id":"mko-polynomial","position":3,"requirement":"optional","rationale":{"zh-Hant":"把多項式視為有限支撐的有理係數資料；合併同次項後再讀取係數與次數。","en":"A polynomial is finitely supported rational-coefficient data; combine like powers before reading coefficients or degree."}},{"id":"mko-factorization","position":4,"requirement":"optional","rationale":{"zh-Hant":"因式分解是在指定係數域中把多項式寫成因子乘積；驗收比較全部係數而不是若干代入值。","en":"Factorization writes a polynomial as a product in a declared coefficient field. Validation compares all coefficients rather than a few evaluated values."}},{"id":"mko-quadratic-equation","position":5,"requirement":"optional","rationale":{"zh-Hant":"對非零二次係數的實方程，用判別式區分實根數，將方程式、根集合與重根分開。","en":"For a real equation with a nonzero quadratic coefficient, the discriminant classifies its distinct real roots. The equation, root set, and repeated roots are kept distinct."}},{"id":"mko-linear-function","position":6,"requirement":"optional","rationale":{"zh-Hant":"實函數 f(x)=mx+b 稱仿射函數；m≠0 時為一次函數，m=0 時為常數函數。","en":"A real function f(x)=mx+b is affine. If m≠0 it has degree one; if m=0 it is constant."}},{"id":"mko-function-graph","position":7,"requirement":"optional","rationale":{"zh-Hant":"固定直角座標系後，實值函數的圖形是全部合法輸入與其唯一輸出組成的有序對集合。","en":"In a fixed Cartesian coordinate system, the graph of a real-valued function is the set of ordered pairs of every permitted input with its unique output."}},{"id":"mko-probability","position":8,"requirement":"optional","rationale":{"zh-Hant":"在非空有限樣本空間上指定非負且總和為一的權重，事件機率為其成員權重之和。","en":"Assign nonnegative weights summing to one on a nonempty finite sample space. An event probability is the sum of the weights of its outcomes."}}]},"title":"七輪代數與機率基礎：冪、恆等式、函數與有限模型"}