{"schema_version":"ocme-site-results-v1","locale":"zh-Hant","page_type":"derivations","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":{"q":"mko-mathematical-representation"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-mathematical-representation-01","title":{"zh-Hant":"數學表徵：判定文字、符號、表格與序對是否表示同一個函數","en":"Mathematical representation: deciding whether words, a formula, tables and ordered pairs represent the same function"},"summary":{"zh-Hant":"固定對象 f:D→ℤ，D={0,1,2,3}，f(x)=2x−1。判定：文字「輸入加倍後減 1」對應 2x−1；表格 T1={(0,−1),(1,1),(2,3),(3,5)} 表示 f；序對集合是 f 的圖形；由兩列 (1,1)、(3,5) 唯一恢復仿射規則；表格 T2 把 (3,5) 換成 (3,6) 後不表示 f，也不表示任何仿射規則；含重複輸入的 T3 不是函數表；定義在 ℤ 上的 g(x)=2x−1 與 f 不是同一個函數；以及表格不提供未列點的值。","en":"Fix the object f:D→ℤ with D={0,1,2,3} and f(x)=2x−1. Decide: the words 'double the input, then subtract 1' correspond to 2x−1; the table T1={(0,−1),(1,1),(2,3),(3,5)} represents f; the set of ordered pairs is the graph of f; the affine rule is recovered uniquely from the two rows (1,1) and (3,5); the table T2, with (3,5) replaced by (3,6), represents neither f nor any affine rule; T3, with a repeated input, is not a function table; g(x)=2x−1 defined on ℤ is not the same function as f; and a table supplies no values at unlisted points."},"mko_ids":["mko-mathematical-representation"]}],"title":"概念推導導讀"}