{"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-set-membership"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-set-membership-01","title":{"zh-Hant":"集合隸屬：x∈A 是命題，並與 ⊆、= 及程式的成員測試區分","en":"Set membership: x∈A is a proposition, kept apart from ⊆, = and a program's membership test"},"summary":{"zh-Hant":"在型別化語境中，設 A={1,2,3}、B={1,2}、𝓕={{1,2},{3}}（元素是整數集合的集合）、E={n∈ℤ ∣ 2∣n}。判定下列命題的真假並給出理由：2∈A；4∈A；B⊆A；A⊆B；B∈𝓕；{1}∈𝓕；1000000∈E；7∈E。並說明 1∈B 與 B∈𝓕 為何不給出 1∈𝓕，以及程式語言的成員測試為何不能取代集合隸屬的語義。","en":"In a typed context let A={1,2,3}, B={1,2}, 𝓕={{1,2},{3}} (a set whose elements are sets of integers) and E={n∈ℤ ∣ 2∣n}. Decide with reasons whether each holds: 2∈A; 4∈A; B⊆A; A⊆B; B∈𝓕; {1}∈𝓕; 1000000∈E; 7∈E. Also explain why 1∈B and B∈𝓕 do not give 1∈𝓕, and why a programming language's membership test cannot replace the semantics of set membership."},"mko_ids":["mko-set-membership"]}],"title":"Concept derivation guides"}