Is it correct to define nilpotent functions as equivalence classes?

Question

I read in Giordano's paper on Infinitesimal Differential Geometry (http://www.iam.fmph.uniba.sk/amuc/_vol-73/_no_2/_giordano/giordano.pdf , p. 3-5 ) that infinitesimal numbers can be considered as equivalence classes $[h]$ and they can be generated by function, for example, $h(t)=t$.

Next Giordano wrote that if $x(t)=y(t)+o(t)$ for $t$->$0$ then $[x]=[y]$ or $x=y$.

Question: is it correct to define nilpotent functions as equivalence classes as it is defined for real numbers via Cauchy sequences of rational numbers with equivalence classes?

Thanks.