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1、数学常用短语与从句(Phrasesorclausesfrequentlyusedinmathematics)常见的涉及运算的短语或句子1.Differentiatebothsidesoftheequationandweget...Integratebothsidesoftheequationandweget...2.Differentiatingbothsidesoftheequation,weget...Integratingbothsidesoftheequation,weget...3.Add(A)to(B)andwehave…(其中(A)、(B)为某些表达式
2、，如不等式、等式、方程等，下同)4．Subtract(B)from(A)andwehave…5.Multiplyingeachtermoftheequationby…,weobtain…6.Dividingtheequationthroughby...,wehave...7.(A)and(B)togethergive…(A)and(B)togetheryield…(A)and(B)togetherimply…8.Comparing(A)with(B),itiseasytoseethat…9.Substituting(A)into(B),weobtain…10.Eli
3、minating(theparameter)tfrom(A)and(B),wehave…11.Byintroducinganewvariable…,wecanthenrewrite(A)asfollowsByintroducinganewvariable…,wecanthenrewrite(A)inthefollowingform12.Byasimplecalculation,weobtainfrom(A)…定理证明过程中常见的短语和句子1.下面的句型可用来表达“根据什么即可得到什么”的意思Accordingtodefinition,itfollows…Accord
4、ingtohypothesis,itfollows…Accordingtoassumptions,itfollows…Accordingtotheorem(N),itfollows…Accordingtolemma(A),itfollows…Accordingtocorollary(B),itfollows…Accordingtotheremark,itfollows…Accordingtothefactthat…,itfollows…(可以把上面的“accordingto”换成“by”)Since…,itfollows…2.如果一个论断可以通过一些简单运算或简单推
5、理而获得，由于这些运算或推理比较简单，读者可以自行推算，因而只需直接写出论断来，这时可用下面句型：(1)Itiseasytoseethat…Itiseasytoshowthat…Itiseasytoprovethat…Itiseasytoverifythat…Itiseasytocheckthat…(2)Itcaneasilybeseenthat…Itcaneasilybeshownthat…Itcaneasilybeprovedthat…Itcaneasilybeverifiedthat…Itcaneasilybecheckedthat…3.如果所要提及的结论比较
6、显浅，或是众所周知，无需作进一步的证明，这时可用下面句型：(1)Itisclearthat…Itisobviousthat…Itisevidentthat…Itiswell-knownthat…(2)Clearly,…Obviously,…Evidently,…4.为了证明一个定理有时需要引进辅助函数，这时可用下面句型：Letusfirstdefinethefunction…Letusintroduceanewfunction…Letusconsiderthefunction…Letusfirstinvestigatethefunction…Let…Set…Defi
7、ne…Put…Consider…5.在一个定理中，有几个结论需要证明，其中有些结论比较明显，可不用证明，仅需证明余下结论即可，这时可用下面句型：Since(A)and(B)areobvious,weneedonlyprove(C).Since(A)and(B)aretrivial,weneedonlyprove(C).Since(A)and(B)aretrivial,itsufficestoprove(C)6.为了证明一个定理，有时我们并不是直接去证明，而是证明一个新的论断，一旦新的论断得到证明，已给定理不难由此而得证，这时可用下面句型：以下各句用于新的论断被证
