String

Description:

• Given a Set $S$ and a natural number $n\in \mathbb{N}$
  1. $S^n=S\times S...\times S$:
     • a set of length n “strings” ( equivalently ordered tuple) with alphabet $S$.
     • $\{0,1{\}}^3=\{000,001,...,111\}$: set of all possible strings created by using the elements n times.
  2. $S^{\ast }=S^0\cup S^1\cup S^2\cup ...$ where $S^0=\{\varnothing \}$:
     • set of finite length “strings” with alphabet $S$
       • set of all possible strings created by using the elements any nb of times, include 0
       • $\{0,1{\}}^3=\{\varnothing ,0,1,00,01,10,...,\mathrm{1..}\}$:
  3. $[n]$ is the set $\{1,2,...,n-1\}$