[x]是向下取整,{x}=x-[x]是取正的纯小数,[1/x]是向下取整,{1/x}=1/x-[1/x]是取正的纯小数或0,[1/x]=1/x-{1/x}, 其中 0<={1/x}<1lim(x→0+)x[1/x]=lim(x→0+)x(1/x-{1/x})~1-o(x)=1
用夹逼定理x(1/x-1)≤ x[1/x]≤ x·1/x1-x ≤ x[1/x]≤ 1lim(x→0+)1-x=1所以lim(x→0+)x[1/x]=1