I am learning how the Mini-Batch-Gradient-Descent (MBGD) Algorithm works and I came across one thing, that I find a bit weird and dont know how to show this. In the MBGD algorithm we have a loop of $N$ phases. And in each of these phases we are choosing a random permutation on $\{1, \dots, n \}$.
At the end of the algorithm it is then stated, that we only need $\textbf{one}$ random variable $U \sim$ Unif[0,1] to generate these sequence of random permutations $(\sigma_i)_{i \in \mathbb{N}}$, which is the part I do not know how to show.
So I am trying to find a map \begin{align} f:[0,1] \to (S_n)^N, \end{align} with $S_n$ being the symmetric group. But it feels very strange to construct several independent permutations with just one number between 0 and 1. Can anyone give me a hint on how to find the map?