佇數學佮邏chek,直接證明 (direct proof) 是1種直接組合公設,定義,事實,小定理 (lemma),定理來說明1个陳述是正實的抑假的的過程。
過程呢頭1步到甲上尾的結論攏著愛用演繹 (deduction) 的邏chek來進行。用著的邏chek差不多攏是包含全部的 ...(for all) 抑存在 ...(there exists) 的一階邏chek。上捷用著的證明規則是MP (modus ponens),第2捷用的是MT (modus tollens); 邏chek轉換 (transposition) 甘MTP (disjunctive syllogism) 嘛真好用。
尼[修改]
這个例用直接證明來證明雙數家雙數猶是相數。
考慮2个雙數 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle x}
甘 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle y}
。因為因攏是相數,會當共寫做 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle x=2a}
甘 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle y=2b}
,解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle a}
甘 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle b}
是較細的整數。按呢,解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle x+y = 2a + 2b = 2(a+b)}
,也就是講 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle x+y}
是2个倍數, 1个雙數。所以2个雙數家做伙定著嘛是相數。