{"schema_version":"ocme-site-results-v1","locale":"en","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-arithmetic-operations"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-arithmetic-operations-01","title":{"zh-Hant":"四則運算：同一組輸入在 ℕ、ℤ、ℚ 中是否有定義","en":"Arithmetic operations: whether the same inputs give a defined result in ℕ, ℤ and ℚ"},"summary":{"zh-Hant":"取 a=3、b=5。在 ℕ（含 0）、ℤ、ℚ 三個數系中，判定 a+b、a·b、a−b、a÷b 是否有定義；有定義時求出結果，並判定結果屬於哪些數系。再判定 3÷0 與 0÷0 在這三個數系中是否有定義。","en":"Take a=3 and b=5. In each of the number systems ℕ (including 0), ℤ and ℚ, decide whether a+b, a·b, a−b and a÷b are defined; when they are, compute the result and decide which systems it belongs to. Then decide whether 3÷0 and 0÷0 are defined in these three systems."},"mko_ids":["mko-arithmetic-operations"]}],"title":"Concept derivation guides"}