Example 6

The greatest integer function [x], shown in Figure 3.4.10, is defined by [x] = the greatest integer n such that n ≤ x.

Thus

[x] = 0 if 0 ≤ x < 1,

[x] = 1 if 1 ≤ x < 2,

[x] = 2 if 2 ≤ x < 3,

and so on. For negative x, we have

[x] = -1 if - 1 ≤ x < 0, [x] = -2

if -2 ≤ x < -1,

and so on.

Figure 3.4.10