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Topic: Greatest integer function

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	Idempotent - Wikipedia, the free encyclopedia
		For example, the greatest integer function is idempotent as a function from the set of real numbers to the set of integers.
		In this case, function composition (denoted "o") is a binary operation on X, and a function f : X → X is idempotent as a unary operator if and only if f o f = f, that is, if and only if f is an idempotent element of this binary operation.
		Less trivial examples are the absolute value function of a real or complex argument, and the greatest integer function of a real argument.
	en.wikipedia.org /wiki/Idempotent (827 words)

	greatest integer function (Site not responding. Last check: 2007-10-16)
		In mathematics, the floor function is the function defined as follows: for a real number x, floor(x) is the largest integer less than or equal to x.
		The floor function is not continuous, but it is upper semi-continuous.
		A closely related mathematical function is the ceiling function, which is defined as follows: for any given real number x, ceiling(x) is the smallest integer no less than x.
	www.yourencyclopedia.net /Greatest_integer_function.html (318 words)

	Mathematics - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-16)
		The study of structure starts with numbers, first the familiar natural numbers and integers and their arithmetical operations, which are recorded in elementary algebra.
		The modern fields of differential geometry and algebraic geometry generalize geometry in different directions: differential geometry emphasizes the concepts of functions, fiber bundles, derivatives, smoothness and direction, while in algebraic geometry geometrical objects are described as solution sets of polynomial equations.
		Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions, laying the groundwork for quantum mechanics among many other things.
	encyclopedia.learnthis.info /m/ma/mathematics.html (2172 words)

	1.4 - Graphs of Functions
		A function is increasing on an open interval if the function rises (positive slope) on the interval as you move from left to right.
		A function is constant on an open interval if the function remains constant (horizontal line segment) on the interval as you move from left to right.
		The greatest integer function is often called the Integer function (or Floor in upper level mathematics), and is abbreviated INT on the calculator.
	www.richland.edu /james/lecture/m116/functions/graphs.html (930 words)

	MAT 117 Test 1 Concepts - Spring 2002 (Site not responding. Last check: 2007-10-16)
		Be able to use functional notation to calculate the value of a function at a given point or for a given expression.
		Be able to solve applications involving the greatest integer function (such as the cost of a taxi--in the homework).
		Be able to rewrite the equation for a basic function that has been transformed by a horizontal and/or vertical shift or reflection and by a vertical stretch/compression.
	fym.la.asu.edu /%7Efym/mat117/test1concepts-fall2003.html (275 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-16)
		The mod function is defined as the amount by which a number exceeds the largest integer multiple of the divisor that is not greater than that number.
		The fact is that there is no definition of "integer division" in math; rather, we divide and apply the greatest integer function or some variation of it to the resulting rational number, depending on our needs.
		Integer division is a formulation of computer languages, and they define it for their own use.
	www.mathforum.org /dr.math/problems/anne.4.28.99.html (2075 words)

	Untitled Document
		In this project we consider the equation dy/dt = [t-y] where [x] is the greatest integer function, this equation isn’t part of the standard curriculum in differential equations.
		Combining the experimental methods, function fitting, and data collection aspects of mathematical modeling we examine the solutions of this equation at initial conditions [Y (0)’s] in the interval [-10,10] where t is a dependent variable.
		One of the ways we used to explain the equation was to solve the equation dy/dt=t-y without the use of the greatest integer function.
	www.edcenter.sdsu.edu /cso/cso2001/diffeq-hau/project.html (481 words)

	Greatest Integer Function (Site not responding. Last check: 2007-10-16)
		The greatest integer function, denoted by int, is defined as follows:
		The greatest integer function is found in the catalog.
		We are now ready to view a graph of the greatest integer function.
	www.prenhall.com /divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/desc_pages/greatestintegerfunction.html (213 words)

	Algebra II: Graphs and Functions - Math for Morons Like Us
		One way to tell if a graph is a function is the vertical line test, which says if it is possible for a vertical line to meet a graph more than once, the graph is not a function.
		When a function is an equation, the domain is the set of numbers that are replacements for x that give a value for f(x) that is on the graph.
		The greatest integer function, y = [x] is defined as follows: [x] is the greatest integer that is less than or equal to x.
	library.thinkquest.org /20991/alg2/graphs.html?tqskip1=1&tqtime=0722 (943 words)

	Graphing and Mathematical Models
		Most of these functions also go through (-1, -1), and all of those are odd functions, except for the greatest integer function (Can you see why it is not symmetric with respect to the origin?).
		The remaining functions are even functions and so go through (-1, 1), except for the square root function.
		In the previous section, we saw that the identify, square, and absolute value functions are "symmetric" with respect to scaling; that is, a horizontal and vertical scale are directly related.
	campus.northpark.edu /math/PreCalculus/Functions/Graphing/Model/index.html (774 words)

	Section Notes (Site not responding. Last check: 2007-10-16)
		For example, 'f(x)=2x+3 for x>0' means that even though the function is mathematically defind for all x, you want to consider only positive values.
		If a function is describing a relationship where there are natural considerations for the variables, then the domain can be determined from that context.
		(b) When determining where a function is increasing or decreasing, remember that you are looking for all the values of x, typically an interval on the x-axis, that correspond to the behavior.
	www.austincc.edu /lrosen/1314/section_notes/unit2.htm (303 words)

	TI-82 Users Guide
		This is the greatest integer function you may have studied in school.
		For negative values, the greatest integer function drops down to the next integer lower than the value, but for -3.2, the next lower integer IS -4.
		These are the numbers 3x+2 for x=1,2,3,and 4 so one method would be to make the integers from one to four, then put them into the function 2x+3… like this 3(int(4*rand+1))+2.
	www.pballew.net /ti_1.html (746 words)

	Mathwords: Floor 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
		Ceiling function (also known as least integer function)
	www.mathwords.com /f/floor_function.htm (46 words)

	Graphing the Greatest Integer function on the TI-86
		The greatest integer function (also called a step function) is actually a piecewise defined function with a special definition.
		This function is the greatest integer less than or equal to x.
		Since this is a piecewise function you should use DOT mode.
	www.math.lsu.edu /%7Eneal/TI_86/graphing/special_graphs/greatest_integer/greatest_integer.htm (73 words)

	PlanetMath: floor
		The floor function is the greatest integer less or equal than its argument.
		On some texts however, it is sometimes seen the bracket notation to denote floor function (although they actually work with integer part) so it is sometimes also called bracket function
		The notation for floor and ceil was introduced by Iverson in 1962 [1].
	www.planetmath.org /encyclopedia/Floor.html (108 words)

	Re: Piecewise functions (Site not responding. Last check: 2007-10-16)
		If it is a floor function or greatest integer function the top part of the [] is missing.
		The function has a closed circle on the integers and is a horizontal line from the circle to the next greatest integer that ends the line with an open circle.
		If this is a ceiling function or least integer function the bottom part of the[] are missing.
	www.mathguide.com /bbs/Messages2003/4060.html (232 words)

	Date Algorithms - Gregorian or Julian date to Julian Day Number - Algorithm Development (Site not responding. Last check: 2007-10-16)
		Here [x] is the greatest integer function, that is, [x] is the greatest integer that is not greater than x.
		For positive numbers, the greatest integer is the same as a function which truncates any fractional part of a number.
		Suppose, for example, that the function is to have the form (AX+B)\32 so that shifts can be used in the binary representation to implement integer* division.
	vsg.cape.com /~pbaum/date/jdalg.htm (1074 words)

	College Algebra Tutorial on Graphs of Functions Part II
		Determine the intervals on which a function is increasing, decreasing or constant by looking at a graph.
		Greatest integer that is less than or equal to x.
		For example, int(5) = 5, int(5.3) = 5, int(5.9) = 5, because 5 is the greatest integer that is less than or equal to 5, 5.3, and 5.9.
	www.wtamu.edu /academic/anns/mps/math/mathlab/col_algebra/col_alg_tut32_graphfun2.htm (2999 words)

	Math 116 - Chapter 4 Study Guide
		The greatest integer of any value between 3 and 4 is 3, so the answer is 3.
		The greatest integer function is symbolized using the double bracket.
		For each exponential function, describe how the graph shown differs from the basic exponential graph (give its transformation) and then write an equation for the graphed function.
	www.richland.edu /james/spring04/m116/m116-s04.html (375 words)

	Date Algorithms - Julian Day Number to Gregorian or Julian date - Algorithm Development (Site not responding. Last check: 2007-10-16)
		First, notice that this difference function has the same value if a multiple of 400 is added to Y; i.e., only the values of Y modulo 400 with values between 0 and 399 need be examined.
		In order for our approximation to be valid, the error function must have values that are greater than or equal to 0 and less than 1 so that applying the greatest integer function to it produces a result of zero.
		This function was examined as part of algorithm development for converting from a Gregorian or Julian Date to the corresponding Julian Day number and will not be reproduced here.
	vsg.cape.com /~pbaum/date/injdalg.htm (2540 words)

	Unit 1 Functions and their Graphs 1.4-1.7
		We continue our focus on the definition of a function, how to graph a function, and the relationship of functions and their graphs as we learn to analyze a function in the next section.
		You should be able to identify the domain and the range from a graph of the function, and for many functions be able to identify the domain and the range from analyzing where the function exits agebraically.
		This section explores the relation between functions and how their graphs are shifted vertically or horizontally, and stretched.
	www.distancemath.com /unit1/funct3.htm (719 words)

	Untitled Document (Site not responding. Last check: 2007-10-16)
		The graph demonstrates from where this function was also labeled the "step" function.
		Since [bx + c] is always rounded down to the nearest integer, the z in the linear equation will not vary as much as x did in the previous linear equation example.
		In this spreadsheet example, z will in fact remain the same whole integer for ten points since the difference between each original x is 0.1.
	www.auburn.edu /~altense/Writeup1/gengif.htm (248 words)

	Integer -- integer (v. lat.: integer unberührt, unversehrt) bedeutet u... (Site not responding. Last check: 2007-10-16)
		Integer bezeichnet einen Datentyp, der in fast allen Programmiersprachen verfügbar ist.
		Ein Integer repräsentiert eine Ganzzahl mit Vorzeichen, wobei es in den meisten Programmiersprachen auch vorzeichenlose Integer-Typen gibt.
		reconstruction case, where a novel systematic investigation of the filter bank properties for all integer subsampling rates is carried out...
	ganzzahl.exsudo.de (252 words)

	The Prime Glossary: floor function (Site not responding. Last check: 2007-10-16)
		The floor function of x, historically called the greatest integer function, is the greatest integer less than or equal to x.
		(a notation that was suggested by Iverson in 1962) to differentiate it from the ceiling function.
		Examples: [3.14159]=3, [-3.14159]=-4, and [log(n)/log(10)]+1 is the number of digits in the decimal expansion of the positive integer n.
	primes.utm.edu /glossary/page.php?sort=FloorFunction (75 words)

	Untitled Document (Site not responding. Last check: 2007-10-16)
		A spreadsheet is an excellent way to set up a function and observe the various numerical changes as well as the graphical representation.
		Now let's look at a different function, the greatest integer function y = a[bx + c] +d, where the brackets [] denote the "floor function" or the "greatest integer function" which rounds the resulting sum, difference, product or quotient down to the nearest whole integer.
		For each of the spreadsheets and graphs of the greatest integer function I chose x to begin at a negative number and for the "step" between each x to be 0.1.
	www.auburn.edu /~altense/writeup1.htm (486 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-16)
		Date: 09/27/98 at 18:10:45 From: Laura Subject: Greatest integer function I am in 11th grade pre-calculus.
		I am familiar with the greatest integer function of y=[x], but I do not know how to go about solving [y]=[x].
		Date: 09/27/98 at 18:30:56 From: Doctor Pat Subject: Re: Greatest integer function Laura, This is an unusual question, but interesting.
	www.forum.swarthmore.edu /dr.math/problems/laura9.27.98.html (324 words)

	Chapter 1
		The concept of a function is very important mathematically and we will spend some time working with functions and performing operations with them.
		To graph with the calculator, the greatest integer function is usually denoted by int.
		Function Composition: Instead of our elements being numbers as they were with addition and multiplication, now our elements are functions and the operation is composition.
	www.octech.edu /icourses/math/mat110/Review/Chapter%201.htm (1947 words)

	Quiz 2a – 2 (Site not responding. Last check: 2007-10-16)
		Recall that an absolute value function changes the sign of a number to positive.
		The absolute value function is the distance formula for numbers.
		Check that it is a function using the Vertical Line Test.
	sierra.nmsu.edu /mlc/185q2a.htm (230 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		The Greatest Integer Function, symbolized by brackets, is defined as follows: if n is an integer and if EMBED Equation.2 , then [x] = n.
		Proper divisors of an integer are divisors that are less than the integer itself.
		The greatest lower bound of a set is the largest number which is less than or equal to all the elements of the set.
	www.mathleague.org /someidea.doc (780 words)

	Grace User's Guide (for Grace-5.1.18)
		Choosing to load the function is almost similar to load the fitted values except that you choose yourself the boundaries and the number of points.
		The grace_np library is a set of compiled functions that allows you to launch and drive a Grace subprocess from your C or Fortran application.
		Functions are provided to start the subprocess, to send it commands or data, to stop it or detach from it.
	plasma-gate.weizmann.ac.il /Grace/doc/UsersGuide.html (11575 words)

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