Hello again :)

Recently I was solving problem with integers a[i] which involved two operations a[i] //= 2 and a[i] -= 1. And I read that it is equivalent that when we are performing these operations, to consider a[i] as a double, transforming a[i] //= 2 to a[i] / 2, and then at the end taking the floor.

This is a little obvious, but nevertheless very surprising to me. Can someone prove it?