{"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-variable-expression"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-variable-expression-01","title":{"zh-Hant":"變數與代數式：式子的值由取值、作用域與數系共同決定","en":"Variables and expressions: a value depends on the assignment, the scope and the number system"},"summary":{"zh-Hant":"設 E=x+1、F=(x+1)÷2、H=Σ_{x=1}^{3}(x+1)。(1) 在 ℤ 中求 E 在 x=2 與 x=5 的值，並證明 E 沒有與 x 無關的固定值；(2) 求 F 在 x=4 時於 ℚ 與 ℤ 中的值；(3) 在外部指定 x=5 時求 H；(4) 判定 (x+1)+x 與 2x+1、x·x 與 2x 在 ℤ 上是否等價；(5) 區分表達式 x+1 與方程 x+1=3，並求方程在 ℤ 中的解集。","en":"Let E=x+1, F=(x+1)÷2 and H=Σ_{x=1}^{3}(x+1). (1) In ℤ, evaluate E at x=2 and at x=5 and prove that E has no fixed value independent of x; (2) evaluate F at x=4 in ℚ and in ℤ; (3) evaluate H when x=5 is assigned from outside; (4) decide whether (x+1)+x and 2x+1, and whether x·x and 2x, are equivalent on ℤ; (5) distinguish the expression x+1 from the equation x+1=3 and find the solution set of the equation in ℤ."},"mko_ids":["mko-variable-expression"]}],"title":"Concept derivation guides"}