浅谈中学数学中的反证法摘要：反证法在数学中是一种非常重要的间接证明方法，它被称为“数学家最精良的武器之一”，又称为归谬法、背理法。反证法亦称“逆证”。其不仅是一种论证方法，对提升学生创新性思维能力与概念思维能力具有积极作用从某种角度可以说，反证法还是一种思维方式，其还能拓展学生的解题思路，从而使学生形成良好的数学思维。反证法在中学数学中有着广泛的应用，如今学生在运用反证法解题中，基础一般的学生会受到思维能力的限制，如果能恰当的使用反证法，在一些有难度的题目上也许能够得到解决。所以本文首先会叙述反证法的产生，具体阐述反证法的定义，即反证法的概念、分类、科学性，介绍逆证在中学数学中的实际运用并论述了逆证应用的具体需要注意的一些问题。关键词：反证法；中学数学；应用；OntheProofbyContradictioninMiddleSchoolMathematicsAbstract：Proofbycontradictionisaveryimportantindirectproofmethodinmathematics,itiscalled"oneofthemostsophisticatedweaponsofmathematicians",alsoknownasreductiontoabsurdity,unreasonablemethod.Proofbycontradictionisnotonlyanargumentationmethod,butalsoawayofthinking.Itplaysanextremelyimportantroleincultivatingandimprovingstudents'logicalthinkingabilityandcreativethinkingability.Itcanalsoexpandstudents'thinkingofsolvingproblems,sothatstudentscanformgoodmathematicalthinking.Anyway,themethodhasbeenwidelyusedinmiddleschoolmathematics.Nowadays,whenstudentssolveproblemswiththemethodofproofbycontradiction,thestudentswithgeneralfoundationarelimitedbytheirthinkingability.Ifthemethodofproofbycontradictioncanbeusedproperly,theymaybeabletosolvesomedifficultproblems.Therefore,thispaperwillfirstdescribethesourceofproofbycontradiction,specificallyelaboratethedefinitionofproofbycontradiction,thatis,theconcept,classificationandlogicalbasisofproofbycontradiction,introducetheapplicationofproofbycontradictioninmiddleschoolmathematicsandexplaintheproblemstobenoticedintheapplicationofproofbycontradiction.Keywords：proofbycontradiction;Middleschoolmathematics;Application;目录目录浅谈中学数学中的反证法.........................................................11引言.........................................................................................12反证法的产生.........................................................................12.1古希腊的反证法...................................................................12.2中国古代数学中的反证法.................................................23反证法的定义与步骤.............................................................23.1反证法的定义.....................................................................23.2反证法的解题步骤.....................................................................................................24反证法的分类与科学性.........................................................44.1反证法的分类.......................................................................44.1.1归谬法例题.........................................................................44.1.2穷举法例题.........................................................................44.2反证法的科学性....................................................................54.2.1反证法的理论依据...........................................................54.2.2反证法的可信性...............................................................54.3为什么要使用反证法...........................................................65反证法在中学数学中的应用..................................
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