数学专业英语2-11,2-12.ppt

NewWords&Expressions:assert断言,:introductiontopredicatesandquantifiersDifficultpoints:specialterminologypeculiartoprobabilitytheoryRequirements:。。Statementsinvolvingvariables,suchas“x>3”,“x+y=3”,“x+y=z”-APredicates包含变量的语句,比如“x>3”,“x+y=3”,“x+y=z”常出现在数学论断和计算机程序中。,则不能判定该语句是真是假,本节要讨论由这种语句生成命题的方法。Thestatement“xisgreaterthan3”,thevariables,“x大于3”分成两部分,第一部分,变量,是语句的主语。Thesecondpart-thepredicate,“isgreaterthan3”-,谓语,“大于3”,指的是语句主语具有的性质。Wecandenotethestatement“xisgreaterthan3”byP(x),wherePdenotesthepredicate“isgreaterthan3”“x大于3”记为P(x),其中P表示谓词“大于3”,而x是变量。ThestatementP(x),thestatementsP(x)(x)也称为命题函数P在x点处的值。一旦赋予变量x一个值,语句P(x)就成为一个命题,有了真假值。Whenallthevariablesinapropositionalfunctionareassignedvalues,,thereisanotherimportantway,calledquantification,,结果语句就有了真假值。但是还有另外一种方式,称为量词化,可从命题函数中得到命题。11-BQuantifiersTwotypesofquantificationwillbediscussedhere,namely,,也就是全称量词化和存在量词化。Manymathematicalstatementsassertthatapropertyistrueforallvaluesofavariableinaparticulardomain,,性质对论域这个特定领域内变量的所有值都成立。。TheuniversalquantificationofapropositionalfunctionisthepropositionthatassertthatP(x)istrueforallvaluesofxintheuniverseofdiscourse.