Set

Let $S=\{s_1< s_2<~...< s_{N}\}$ be a finite and strictly ordered set of $\mathbb{R}$ :

$$S = \{s_i \in \mathbb{R}, i \in [1,N] ~|~ \forall(i,j) : i < j \Rightarrow s_i<s_j \}$$

We denote :

• $N$ the cardinality of $S$
• $\mathbb{S}$ the infinite set of such sets ($S \in \mathbb{S})$

$S$ will indifferently be referred to as a $N$-tuple or simply a tuple.