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How to write proofs: a quick guide - GitHub Pages

How to writeproofs:a quick guideEugeniaChengDepartment of Mathematics,University of eugeniaOctober 2004A proof is like a poem,or a painting,or a building,or a bridge,or a novel,or a symphony.\Help!I don'tknow how to writea proof !" Well,didanyoneever tellyouwhata proofis, andhowto goaboutwritingone?Maybe which caseit'snowonderyou' good proof is notsupposedto be somethingwe 'slike writinga poemin a to to know it wellenoughto writepoetryin it, notjustsay \Whichway is it to thetrainstationplease?"Even whenyou know how to do it, writinga proof takes planning,e sketchesbeforestartinga paintingforreal;greatarchitectsmake plansbeforebuildinga building;greatengineersmake plansbeforebuildingabridge;greatauthorsp lantheirnovelsbeforewritingthem; ,greatmathematiciansplantheirproofsin advanceas Whatdoes a proof looklike?

ying leaps instead of earthbound steps. This category includes leaping from one statement to another without justifying the leap leaving out too many steps in between using a profound theorem without proving it (worse) using a profound theorem without even mentioning it For example, spot the ying leap in the following \proof": a(b c) = ab+a( c ...

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