Formal Statement [Step 0]

Definition of a sorting algorithm:

• Input: A list of n objects $A[1], \ldots, A[n]$, and a total order relation ``$\le$'' on objects.
• Here, A[i] refers to the ith object in the list.
• Output: A permutation B of A such that
• $B[1] \le B[2] \le B[3] \le \ldots \le B[n-1] \le B[n]$.