Analyse I (anglais)

When we talk about regular partition $\sigma_n$ of the interval [0,1], we mean the partition whose consecutive points are at distant $\frac 1n$ one from the other, i.e. the partition $\sigma_n \colon =\{ x_0=0< x_1 \colon = \frac 1n < x_2 \colon = \frac 2n < ...< x_i \colon = \frac in < \dots < x_{n}\colon = \frac nn=1\}$.