One very important benefit of having sorted elements is the ability to quickly search through them. If you have a sequence of sorted elements you can use binary search to find if it includes a given element or to find the proper place of a new element in the sorted sequence with time complexity `O(logN)`

. For big enough sequences this is much better than the linear approach of searching through the whole sequence until you find the answer.

- TopCoder tutorial on binary search
- Coderust rundown on Binary search, with visualizations and code examples.