What's confusing me is, when I've a specific Problem, and I need to solve the problem by solving its sub-problems(recursive manner), I'm wondering why we disregarding the solved part problem once solved ? meaning if I have a Problem which its to sort an Array by using for instance QuickSort, lets say I have {1,2,3,4,5,6} and the pivot is 6 which we say that 6 is on its exact place so its sorted, then we are having now sub-problem to solve which is {1,2,3,4,5} ..and then the same thing, 5 is the pivot, and its on the same exact place, so we just ignoring it and saying now we have subproblem which is {1,2,3,4} ..etc , my question why we are neglecting the sorted element and once its sorted we subtract it from the problem? it's like a nullity for us after sorted why?! maybe I'm not good as much good at logic but I believe by your help I could understand it very well.

Maybe if you give me please a real life analogues elaborating that logic(neglecting some parts of the problem and going just to the subproblems) would be much appreciated to get fast learning