288 LIMITS AND FLUXIONS 



logicians independently, which freed the number con- 

 cept from magnitude and established number theory 

 on the concept of order. Chief among the workers 

 in this field were Méray, Weierstrass, Dedekind, 

 and Georg Cantor. It is to them that we owe re- 

 presentations of number, both rational and irrational, 

 which have yielded a much more satisfactory theory 

 of limits, and in that way have vastly improved the 

 logicai exposition of the differential calculus. These 

 theories have brought about the last stages of what 

 is called the aritJunetisation of mathematics. As 

 now developed in books which aim at extreme 

 rigour, the notion of a limit makes no reference to 

 quantity and is a purely ordinai notion. Of this 

 mode of treatment the eighteenth century had never 

 dreamed. 



