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Greatest Integer Function


If x is a real number, we define [x] as follows: 
[x] = n where n is the greatest integer less than or equal to x

Note that n is the first integer to the left of (or equal to) x. For instance,
[0.5] = 0                     [1.8] = 1                      
[π ] = 3                       [e] = 2                          [-2.7] = -3
[- 3.4] = -4                 [- 0.75] = -1                  [-9.3] = -10

The greatest integer function f is defined by f(x) = [x] x R.

The domain of f is R and its range is Z, the set of integers. To draw the graph of

f(x) = [x] we list the x and y coordinates of some points on the graph in the following table.

Values of x

f(x) = [x]

.
.
.

.
.
.

-2 x < - 1

-2

-1 x < 0

-1

0 x < 1

0

1 x < 2

1

2 x < 3

2

.
.
.

.
.
.

Whenever x is between successive integers, the corresponding part of the graph is a segment of the horizontal line. The graph of greatest integer function is given in the figure:





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