Preface（第1页）

Preface

Thepurposeofthislittlebookistoexplain，iwillbefamiliartoeveryoarethevariouskindsofariseandhowtheybehave。Numbersallowparisoweenallmahings，ahandingofnumberswouldbelostinthemodernwsnumericalaretheretogreetusateveryturn。Weshouldrealizehoitetheirfamiliarity，numbershavenophysicalexisteherareabstrasthatweelitheworldwefindourselvesin。Todevelopaclearpictureofhowtheyoperate，itissometimesbettertosiderthemintheirht，withoutreferehingelse。

ThisShortIntroduotarefresherarithmetiorwillthatmuchbesaidooryoftheem。Ratheritspurposeistoexplaihemselvesandthekiheyexhibit。Aglaofchaptersrevealsthatthefirstpartofthebookdealsmainlywithordinaryumbers，whileinthesedhalfwegobeyondthat。Byexplnaturalproblemsthatariseinerdseedtofreelyperformcalseventuallyhastakenus，bystages，intothearenaofthebers，whichistheprinderlyingframeworkformosters。Thismaysoundalittledauntiassured，thehardworkhasalreadybeendoneforyou。

Themoderemdidousgift-edbutratherhasdevelopedovermauries。Therewerelongperiodsof，whichhadtworootcauses。Thefirstwasthelaeffitresentthehatwouldalloulatethem。Thesed，whichwasrelatedtothefirst，hilosophiizierpretationsofvariousypesatheyaremeaningful。Nowadayswearemuchmoresureofourselveswhewedoanddooworryaboutwhehnumbers，makingitpossibletogiveapletepiberworldiatlikethisoisnottosaythatallmysteryhasvanished–farfromit，asyouwilldiscoverasyoureadon。

&erM。Higgins

Cland，2011