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Topic: Natural number object

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Terminal object

	PlanetMath: natural number
		When it is not explicitly specified, one must determine from context whether 0 is being considered a natural number or not.
		The natural numbers form a monoid under either addition or multiplication.
		This is version 11 of natural number, born on 2001-10-19, modified 2002-11-18.
	planetmath.org /encyclopedia/NaturalNumber.html (196 words)

	Natural number - Wikipedia, the free encyclopedia
		Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory.
		The number q is called the quotient and r is called the remainder of division of a by b.
		Two generalizations of natural numbers arise from the two uses: ordinal numbers are used to describe the position of an element in an ordered sequence and cardinal numbers are used to specify the size of a given set.
	en.wikipedia.org /wiki/Natural_number (1938 words)

	number. The Columbia Encyclopedia, Sixth Edition. 2001-05
		Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their members can be matched in a one-to-one correspondence.
		The real numbers are those representable by an infinite decimal expansion, which may be repeating or nonrepeating; they are in a one-to-one correspondence with the points on a straight line and are sometimes referred to as the continuum.
		Numbers of the form z = x + yi, where x and y are real and i = [radical]-1, such as 8 + 7i (or 8 + 7[radical]-1), are called complex numbers; x is called the real part of z and yi the imaginary part.
	www.bartleby.com /65/nu/number.html (513 words)

	JavaScript Kit- Math Object
		The constant of E, the base of natural logarithms.
		Returns a pseudorandom number between 0 and 1.
		Math.random() //returns random number between 0 and 1, such as 0.634343434...
	www.javascriptkit.com /jsref/math.shtml (160 words)

	NaturalNumbers - PineWiki
		These correspond to all possible sizes of finite sets; in a sense, the natural numbers are precisely those numbers that occur in nature: one can have a field with 0, 1, 2, 3, etc. sheep in it, but it's hard to have a field with -12 or 22/7 sheep in it.
		You are a number theorist, and you don't want to have follow "Let n be a natural number..." with "(except zero)" in every theorem you write.
		In SetTheory, a natural number is defined as a finite
	pine.cs.yale.edu /pinewiki/NaturalNumbers (955 words)

	NPS: Nature & Science » Natural Sounds
		Both natural and human sounds may be desirable and appropriate in a soundscape, depending on the purposes and values of the park.
		The number of pressure variations per second in the air or the number of peaks and troughs in the sound wave is called the frequency of the sound and is expressed in hertz (Hz).
		As an object vibrates it creates sound waves and as it vibrates harder, the height of the wave, or the distance between the peaks and troughs in the wave, increases.
	www.nature.nps.gov /naturalsounds/index.htm (983 words)

	Philosophy of Mathematics
		On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
		If natural numbers are mathematical objects, as the realist contends, and if all mathematical objects are sets, then there is a fact concerning which sets the natural numbers are.
		There is no more to being the natural number 2 than being the successor of the successor of 0, the predecessor of 3, the first prime, and so on.
	www.wordtrade.com /science/philosophymathematicsR.htm (1791 words)

	Prime number - ExampleProblems.com
		In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself.
		A natural number that is greater than one and is not a prime is called a composite number.
		The prime number theorem says that the proportion of primes less than x is asymptotic to 1/ln x (in other words, as x gets very large, the likelihood that a number less than x is prime is inversely proportional to the number of digits in x).
	www.exampleproblems.com /wiki/index.php/Prime_number (3311 words)

	Whitepapers HTML Version - Using Higher Performance Databases in Advanced Intelligent Networks (Site not responding. Last check: 2007-10-09)
		The numbers in brackets indicate the minimum and maximum number of connections between objects of those classes.
		For example, two of the most important transaction characteristics are the number of simultaneous readers and the number of simultaneous updaters that access the database.
		Furthermore, since the objects on the page stored in application memory are clustered, the application will have related objects already in memory for the next transaction, further decreasing disk access.
	www.objectivity.com /WhitePapers/Advanced-intelligent-network.shtml (3515 words)

	Number: What Is "This Many?" -- Platonic Realms MiniText
		However, negative numbers can be very handy for calculations involving debt, and the Italians (who invented banks) were the first to recognize their importance in finance and to use them for that purpose.
		What it says is, the set of rational numbers is the set consisting of all numbers of the form p divided by q, where p and q are elements of the set of integers and q is not zero.
		Historically, the rational numbers are nearly as old as the natural numbers.
	www.mathacademy.com /pr/minitext/number (3230 words)

	Peano axioms Summary
		In order to do this, the negative integers are defined as the additive inverses (or opposites) of the natural numbers and the rational numbers of the form 1/n, where n is not 0, are defined as multiplicative inverses of the natural numbers and their opposites.
		In this way, we expand the number system to include all the integers and all the rational numbers of the form 1/k, where k is not 0.
		The set N is the set of natural numbers; it is sometimes denoted by the Greek letter ω, especially in the context of studying ordinal numbers.
	www.bookrags.com /Peano_axioms (3389 words)

	Natural number object - Wikipedia, the free encyclopedia
		In category theory, a natural number object (nno) is an object endowed with a recursive structure similar to natural numbers.
		Nnos in CCCs or topoi are sometimes defined in the following equivalent way (due to Lawvere): for every pair of arrows g : A → B and f : B → B, there is a unique h : N × A → B such that the squares in the following diagram commute.
		Nnos can be used for nonstandard models of type theory in a way analogous to non-standard models of analysis.
	en.wikipedia.org /wiki/Natural_number_object (381 words)

	Some Web Object Model Construction Technologies
		Object technology is seen as a particularly-convenient way of adding functionality (e.g., behavior) to the Web, both by adding the behavior provided by objects to the static content of HTML, and by allowing Web clients and servers, through distributed object technology, to access other computing resources.
		An object's state representation is used to hold various pieces of data that are operated upon by the object's operations, and that retain information from one operation invocation to the next.
		An object's interface is an API that determines which object methods and state are revealed to external clients, and that conceals (encapsulates) the details of the actual method and state representations from those clients.
	www.icc3.com /ec/objects/modeling3.htm (10686 words)

	Natural Food - Meat and human evolution
		There is some evidence that naturally occuring anti oxidants in food help to dampen down the effects of the foreign chemical agent we are unwittingly exposed to.
		Saturated fats are evolutionarily natural, whether derived directly from animal fat, or whether the body has to construct its saturated fats from the nuts, tubers, and seeds that it eats.
		In addition, natural, grass fed beef has a higher anti oxidant capacity than feedlot beef, which means the grass fed meat cuts retain their red color longer.
	www.naturalhub.com /natural_food_guide_meat.htm (2982 words)

	Using Natural Language in Software Development
		First, the nature of the problem is considered - the ambiguity and vagueness inherent in natural language and the need for precision and comprehension in formal models.
		Natural conceptual models retain much of the character of the natural language from which they were derived.
		The mapping from simplified natural language to conceptual models (and vice-versa) needs to be relatively obvious, so that people can readily comprehend the conceptual models and see their linkage back to the natural language from which they originated.
	www.educery.com /papers/rhetoric/road (7757 words)

	Object Pascal - Fundamental Data Types
		A word, which is a group of 16 contiguous bits or 2 bytes is used to represent a natural number that uses twice the space of a short integer.
		If you want to use a natural number whose value is very large, you can use the Int64 keyword to declare it.
		Previous versions of Object Pascal were also using the Comp data type that would be used to store numbers that range between –263+1 and 263 –1.
	www.functionx.com /objectpascal/Lesson05.htm (1995 words)

	Jules Henri Poincaré [Internet Encyclopedia of Philosophy]
		Another interesting aspect of Poincaré's study is the real nature of the distribution in phase space of stable and unstable points, which are so mixed that he did not try to make a picture of their arrangement.
		If the successor of natural number a is equal to the successor of natural number b, then a and b are equal.
		To determine the corresponding number it is necessary to insert this phrase in alphabetical order; but such an operation modifies the number associated with the already classified points whose defining phrase follows, in alphabetical order, the new phrase.
	www.iep.utm.edu /p/poincare.htm (3565 words)

	Object (Stanford Encyclopedia of Philosophy)
		In this remark, a certain extremely general, topic-neutral use of ‘object’ is singled out, a use in which the expression is treated as equivalent to (equally neutral) uses of ‘term’, ‘entity’, ‘unit’, ‘individual’, and ‘thing’.
		Wherever the word ‘object’ (‘thing’, ‘entity’, etc.) is rightly used, it is expressed in logical symbolism by the variable name.
		The fundamental spirit of the object-thesis involves affirming simply that our talk is indeed talk exclusively of objects—that we may speak of objects in the plural as well as in the singular, and that plural talk of objects is talk of the very same category of things as is talk of objects in the singular.
	plato.stanford.edu /entries/object (3156 words)

	Servertec - Number Object
		Returns a number rounded to the smallest whole number greater than or equal to it.
		Returns a number rounded to the largest whole number less than or equal to it.
		Returns whether the specified value is a number infinitely large in magnitude.
	www.servertec.com /products/iscript/docs/Number.html (170 words)

	Life Path Number, Numerology, Numerology Software, Free Numerology
		MB Free Life Path Number Software is an interactive and easy to use software, which talks about the life path number, or simply the sum of your birth date.
		MB Free Life Path Number Software helps you to calculate your life path number which refers to your native in-born qualities that would accompany you throughout your life.
		This number states who you are at the time of birth and all about your inborn traits.
	www.lifepathnumber.info /in-born-qualities/numerology/life-path-number.html (165 words)

	Answers and Explanations -- Imaginary Numbers: How To Show They Exist
		After all, it's a pair of natural numbers, 3 and 1 (representing the ratio "3 to 1"), not a single natural number.
		Since numbers are just abstract concepts anyway, and since natural numbers a and fractions of the form a/1 are completely identical as far as their arithmetic behaviour is concerned, it is perfectly legitimate to view them as just two different representations of the same underlying concept.
		Since numbers are just abstract concepts anyway, and since real numbers a and complex numbers of the form (a,0) are completely identical as far as their arithmetic behaviour is concerned, it is perfectly legitimate to view them as just two different representations of the same underlying concept.
	www.math.toronto.edu /mathnet/answers/imagexist.html (1401 words)

	Abstracts (Site not responding. Last check: 2007-10-09)
		However, it is often unsatisfying to call a randomly selected object a ``construction'', as no explicit description is given.
		Abstract: The analogue of the Erdos-Turan conjecture, about the unboundedness of the number of representations by a basis of the natural numbers, is known not to hold in arbitrary semigroups.
		Let A be an infinite sequence of non-decreasing positive integers such that the number of elements of A with values between 1 and n is at least Cn for all sufficiently large n.
	www.theoryofnumbers.com /CANT/2004/abstracts.htm (1708 words)

	HubbleSite - NewsCenter - Natural Lenses in Space Stretch Hubble's View of the Universe (05/13/1999) - Introduction
		A Hubble telescope survey of the sky has uncovered exotic patterns, rings, arcs, and crosses that are all mirages produced by a gravitational lens, nature's equivalent of having a giant magnifying glass in space.
		A gravitational lens is created when the gravity of a massive foreground object, such as a galaxy or a fl hole, bends the light coming from a far more distant galaxy directly behind it.
		This "gravitational muscle" focuses the light to give multiple or distorted images of the background object as seen by the observer.
	hubblesite.org /newscenter/archive/releases/1999/18 (124 words)

	Good Math, Bad Math : Categorical Numbers
		To sum up: Peano arithmetic is based on a definition of the natural numbers in terms of five fundamental properties, called the Peano axioms, built on "0", a successor function, and induction.
		The result returned by successor is also a number, all numbers have a unique successor, and no number has 0 as a successor.
		What the peano axioms do is define a sequence of "objects", each of which has exactly one "successor", etc. If you look at, for example, the definition of addition, it never says "add one" to anything; it's defined in terms of successor.
	scienceblogs.com /goodmath/2006/08/categorical_numbers.php (1704 words)

	Some Useful Built-in Language Objects and Functions
		Write a function that formats a number given a specified number of places after the decimal point.
		The function should accept two numeric arguments: the number to be formatted and the number of digits after the decimal point.
		This is not a true object, however, so you don't ever refer to a "Global" object - instead you just use the properties and methods directly.
	faculty.washington.edu /kkbarker/ClassPages/Js/LanguageObjects.html (1374 words)

	naked eye object Comparison Table (Site not responding. Last check: 2007-10-09)
		Next physical object: natural object Up: physical object Previous physical object: artifact
		originally to catalog all objects which could be confused with a comet
		Subdivided according to the openness of the spiral arms as Sa spiral, Sb spiral or Sc spiral.
	www.site.uottawa.ca:4321 /astronomy/nakedeyeobject_table.html (527 words)

	Data Structures and Algorithms I Lab 5
		If a data member is static, then all objects (of this class type) share access to the one memory location that holds that static data member's value.
		Various operations are defined to change the value of a natural number object.
		You should find that the id numbers are equal: If you don't supply a copy constructor explicitly, then C++ uses a default that simply copies the individual bits of the original to make the copy.
	www.cs.uakron.edu /~xiao/dsai/Lab05.html (1061 words)

	Ask-A-Link Games - play acrade, card and board games: backgammon, domino, mahjong, solitaire, pool, cribbage for free ...
		The object of the game is to score as many points as possible by collapsing the groups of 2 or more adjacent sea-creatures.
		The object of the game is to score as many points as possible by collapsing vertical or horizontal groups of 3 or more similar tiles.
		Every meld must contain at least two natural cards, the number of wild cards should not exceed the number of natural card and be less or equal to 3.
	www.askalink.com (813 words)

	IBM Research: DreamSpace: natural interaction
		Users are free to focus on virtual objects and information and understanding and thinking, with minimal constraints or distractions by "the computer", which is present only as wall-sized 3D images and sounds (but no keyboard, mouse, wires, wands, etc.).
		Other systems that use natural interaction are in the works: desks, tables, cars, kitchens, living rooms -- natural objects and environments that also happen to be "smart" and interactive.
		Deviceless natural interfaces are useful (and fun) for a wide range of systems: embedded into your car; embedded into a desktop or workbench; embedded into your kitchen or living room; or embedded into the tabletop at your favorite cafe or diner.
	www.research.ibm.com /natural/dreamspace/index.html (1642 words)

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