Home » Ask & Discuss » Institutes & Courses » Coaching Institutes & Course Material « Back to Discussion

Coaching Institutes & Course Material

New kid on the Block

Joined:	10 Mar 2010
Post:	1

10 Mar 2010 11:59:28 IST

0 People liked this

254

define greatest integer function

None

define greatest integer function

Share this article on:

Comments (3)

Dasvidaniya

Blazing goIITian

Joined: 9 May 2009

Posts: 831

10 Mar 2010 12:20:06 IST

Like 1 people liked this

The greatest integer function of a real number x is represented by [x] or |_x_|.
For all real numbers x, the greatest integer function returns the largest integer less than or equal to x.

In other words, the greatest integer function rounds down a real number to the nearest integer.

More about Greatest Integer Function

Greatest integer functions are piece-wise defined.

The domain of the greatest integer function is the set of real numbers which is divided into a number of intervals like [4, 3), [3, 2), [2, 1), [1, 0), [0, 1), [1, 2), [2, 3), [3, 4) and so on.

Hint: [a, b) is just an interval notation which means a ≤ x < b, where x is a real number in the interval
[a, b).

When the interval is of the form [n, n + 1), where n is an integer, the value of the greatest integer function is n. For example, the value of the greatest integer function is 4 in the interval [4, 3).

The graph of a greatest integer function is not continuous. For example, the following is the graph of the greatest integer function f (x) = |_x_|.

The graph above looks like a stair case (a series of steps). So, the greatest integer function is sometimes called a step function. One endpoint in each step is closed (black dot) to indicate that the point is a part of the graph and the other endpoint is open (open circle) to indicate that the points is Not a part of the graph.

Observe in the graph above that in each interval, the function f(x) is constant. Within an interval, the value of the function remains constant. For example, in the interval [–5, –4) the value of the function f(x) remains – 5.

In different intervals, however, the function f(x) can take different constant values.

Greatest integer function is also called floor function

edison

Forum Expert

Joined: 19 Oct 2006

Posts: 7452

10 Mar 2010 14:29:42 IST

Like 1 people liked this

In the above post all fine but

[-8.7] = -9

Greatest Integer Function

A step function of x which is the greatest integer less than or equal to x. The floor function is written a number of different ways: with special brackets or , or by using either boldface brackets [x] or plain brackets [x].

Examples: and .

Dasvidaniya

Blazing goIITian

Joined: 9 May 2009

Posts: 831

10 Mar 2010 14:40:41 IST

Like 0 people liked this

thank u sir...

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team