Selection Sort, Bubble Sort, & Insertion Sort

What is sorting?

Sorting is any process of arranging items systematically. In computer science, sorting algorithms put elements of a list in a certain order.

The most frequently used orders are numerical (according to numbers) and lexicographical (according to letters). Efficient sorting is important for optimizing the efficiency of other algorithms which require sorted input or sort given input as part of their process.

Formal Definition

A list or array is sorted in ascending order if $\forall$ $i$, such that $i \leq n-1$, $A[i]\leq A[i+1]$. Similarly, a list or array is sorted in descending order if $\forall$ $i$, such that $i \leq n-1$, $A[i]\geq A[i+1]$.