title: Big-O running time of sorting vs inserting
body: <p>So if you use quick sort to sort an array you can do it in O(nlogn) using quicksort and then once you sort it, you can insert new elements into the array in O(logn) with a binary-search-esque algorithm. </p>
  
  <p>My question is, is there a way to prove that if you can insert into a sorted array in O(logn) time, then that means that the sorting algorithm would have had to be at least O(nlogn)? </p>
  
  <p>In other words, is there a relationship between the two algorithms' running times?</p>