Show that is the closest integer to the number .x, except when x is midway between two integers, when it is the larger of these two integers.

Solution:Step 1In this problem we are asked to show that the closest integer to the number x is, except when x is midway between two integers, then it is the larger of these two integers.Step 2According to the definition of floor function which is “where n is the maximum of all the integers which are less than or equal to x.” It can be written for every real number x that there is an integer n such that .There are three cases that arises from 1) x is closer to n+1.2) x is closer to n.1) x is midway between n and n+1 i.e .Checking all the conditions...