greatest integer, greatest integer function, step function

Click on the [[x]] image for additional info.

Enter negatives as "-x" rather than "- x" Input a number

The greatest integer function, [x], rounds down to the lower integer or "floor."

There is no formal name for the round up function other than round up or "ceiling."

There is no formal name for the rounds to the nearest integer or multiple.

Some of the html code and Excel functions are listed here. The html math functions (used here) include these & others: Math.ceil() Round up. Math.floor( ) Round down. Math.round( ) Round to the nearest integer. Excel Formulas Include These & Others: =FLOOR.MATH(x,this multiple of y) Rounds x down to the nearest integer that is a multiple of y . =FLOOR.MATH(x) Rounds x down to the nearest integer, [[x]].

IN MATH: 1. n. the function, or rule which produces the "greatest integer less than or equal to the number" operated upon, symbol [x] or sometimes [[x]].

The greatest integer function is a piece-wise defined function.

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

Examples: 
number	|	the greatest integer less than or equal to the number
   x		|	  [x]
   4		|	  [4] = 4
   4.4	|	  [4.4] = 4
   -2		|	  [-2] = -2
   -2.3	|	  [-2.3] = -3

[[x]].gsp Sketchpad -- greatest integer function, also a[[bx+c]] + k
WARNING!! - Geometer's Sketch Pad does not have a greatest integer function.
This graph is a fake and has issues.
piecewise.gsp Sketchpad -- graphs a piecewise defined functions
More Examples of Composite Functions
Absolute Value Function, |x|
What's a Function? - Index on topics like "How Functions Are Composed or Created", "Polynomial & Rational Functions"
$library$ - Function and Relation Library - Many functions w/their features & graphs

IN ENGLISH: 1. as defined above.

APPLICATIONS:

1. Complete given [x], the greatest integer less than or equal to a number.: a.) [6.2] Answers 6; b.) [-6.2] Answers -7
2. List an application, use, of this function.: Answers US postage is sold by weight, a stamp costs a specific price for up through a specific weight.

This is a page from the dictionary MATH SPOKEN HERE!, published in 1995 by MATHEMATICAL CONCEPTS, inc., ISBN: 0-9623593-5-1. You are hereby granted permission to make ONE printed copy of this page and its picture(s) for your PERSONAL and not-for-profit use.

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