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The greatest integer function
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Nevernevergiveup
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The greatest integer function [#permalink] New post  12 Aug 2016, 08:22
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THE GREATEST INTEGER FUNCTION




Image


Definition: This step function is a piece-wise defined function.

The name piece-wise is used to indicated that the function is pieced together, or put together using other functions.




Think of steps. Think of paying sales tax, or income tax, or buying postage stamps.

Think of paying a nice round number for all services or numbers up to the next round number.

Think of the greatest integer less than or equal to the number in question. That's the greatest integer function.

Its symbol is [[x]]. Its graph looks like steps as above.

The function has discontinuities, breaks, going from one "step" to the next. In each interval, the lower endpoint is included (as shown by a colored in circle) and the upper endpoint (as shown by a hollow circle) is not included because it is included in the next "step."




Keypoints:



If the number is an integer, use that integer.

    [4] = 4

    [-2] = -2

If the number is not an integer, use the next smaller integer.

    [4.4] = 4

    [-2.3] = -3



A small table of values

Image
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Balajikarthick1990
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Re: The greatest integer function [#permalink] New post  24 Aug 2016, 22:54
Nevernevergiveup wrote:

THE GREATEST INTEGER FUNCTION




Image


Definition: This step function is a piece-wise defined function.

The name piece-wise is used to indicated that the function is pieced together, or put together using other functions.




Think of steps. Think of paying sales tax, or income tax, or buying postage stamps.

Think of paying a nice round number for all services or numbers up to the next round number.

Think of the greatest integer less than or equal to the number in question. That's the greatest integer function.

Its symbol is [[x]]. Its graph looks like steps as above.

The function has discontinuities, breaks, going from one "step" to the next. In each interval, the lower endpoint is included (as shown by a colored in circle) and the upper endpoint (as shown by a hollow circle) is not included because it is included in the next "step."




Keypoints:



If the number is an integer, use that integer.

    [4] = 4

    [-2] = -2

If the number is not an integer, use the next smaller integer.

    [4.4] = 4

    [-2.3] = -3





A small table of values

Image


Brilliant article. Just to top off a typical caveat in GMAT problem`s.

The Greatest integer function of "-0.9" is "0" and not "-1". We tend to miss this quite often. In the negative scale, the closer a number is to the origin, the bigger it is.

Cheers
Balaji
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Nevernevergiveup
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Re: The greatest integer function [#permalink] New post  28 Oct 2016, 23:05
Balajikarthick1990 wrote:

Brilliant article. Just to top off a typical caveat in GMAT problem`s.

The Greatest integer function of "-0.9" is "0" and not "-1". Nope We tend to miss this quite often. In the negative scale, the closer a number is to the origin, the bigger it is.

Cheers
Balaji


Balajikarthick1990

[-0.9] = -1 and not 0.

you can refer below links

http://www.icoachmath.com/math_dictiona ... ction.html
https://www.youtube.com/watch?v=gZsV-uR6ysg
https://www.youtube.com/watch?v=bGZI9rwWb-Q
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Re: The greatest integer function [#permalink] New post  05 Nov 2017, 19:33
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