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Topic: Natural number

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	Natural number - Wikipedia, the free encyclopedia
		Natural numbers have two main purposes: they can be used for counting ("there are 3 apples on the table"), and they can be used for ordering ("this is the 3rd largest city in the country").
		Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory.
		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 (1844 words)

	Number - Wikipedia, the free encyclopedia
		The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra, the study of abstract number systems such as groups, rings and fields.
		This number is denoted by i, a symbol assigned by Leonhard Euler.
		The existence of complex numbers was not completely accepted until the geometrical interpretation had been described by Caspar Wessel in 1799; it was rediscovered several years later and popularized by Carl Friedrich Gauss, and as a result the theory of complex numbers received a notable expansion.
	en.wikipedia.org /wiki/Number (3699 words)

	Natural number - Wikipedia
		An important property of the natural numbers is that they are well-ordered: every non-empty set of natural numbers has a smallest element.
		The deeper properties of the natural numbers, such as the distribution of prime numbers for example, are studied in number theory.
		Natural numbers can be used for two purposes: to describe the position of an element in an ordered sequence, which is generalized by the concept of ordinal number, and to specify the size of a finite set, which is generalized by the concept of cardinal number.
	wikipedia.findthelinks.com /na/Natural_number.html (639 words)

	Natural number
		A natural number is a non-negative integer: 0, 1, 2, 3, 4,...
		Natural numbers have two main purposes: they can be used for counting ("there are 3 apples on the table"), or they can be used for ordering ("this is the 3rd largest city in the state").
		The deeper properties of the natural numbers, such as the distribution of prime numbers, are studied in number theory.
	www.fact-index.com /n/na/natural_number.html (1096 words)

	Natural number (Site not responding. Last check: 2007-10-21)
		numbers have two main purposes: they can used for counting ("there are 3 apples on the or they can be used for ordering ("this is the 3rd largest city the country").
		Properties of the natural numbers to divisibility such as the distribution of prime numbers are studied in number theory.
		Other mathematicians primarily number theorists often prefer to follow the older and exclude zero from the natural numbers.
	www.freeglossary.com /Whole_number (1646 words)

	Pythagoras - Number
		Number mysticism is not generally associated with "serious mathematics" but from the early Pythagoreans until the 19th century many venerated mathematicians practised some forms of numerology.
		To the Pythagoreans the holiest number of all was the number 10 or the tetractys.
		The discovery which created such a threat to Pythagoreanism was that natural numbers or their ratio are not sufficient when comparing the length of the diagonal of a square to its side.
	www.mathgym.com.au /history/pythagoras/pythnum.htm (2721 words)

	Notes on Mathematics, part I – Number System
		Natural Numbers: The most basic set of numbers, natural numbers are just the set of all positive integers (the number zero is also considered as a natural number by many).
		The result is the rational numbers, the set of numbers of the form a/b, where a and b are integers (and b not equals to zero, of course).
		The set of algebraic numbers consists of all the real numbers that are also the roots of at least one polynomial (of any degree) with rational numbers as its coefficients.
	www.math.psu.edu /tseng/class/sidebar/NumberSystem.htm (787 words)

	[No title]
		From here it can be shown that the natural numbers are equinumerous to all rational numbers by mapping the even natural numbers to the positive rationals, the odd natural numbers to the negative rationals, and 0 to 0.
		Lemma: The natural numbers are equinumerous to the irrational numbers represented by positive square roots.
		Therefore, the natural numbers are equinumerous to the irrational numbers represented by positive whole number roots of rational numbers.
	www.public.iastate.edu /~joefish/proof.doc (382 words)

	Natural Number (Site not responding. Last check: 2007-10-21)
		And like a growing number in the Segway subculture, he's used it as part of his everyday life - to dance at the wedding, fish near the Arctic Circle, to argue...
		The number of new oil and natural gas well permits issued in Utah is soaring.
		Under this definition, there are exactly n elements (in the naive sense) in the set n and n ≤ m (in the naive sense) iff n is a subset of m.
	www.wikiverse.org /natural-number (1563 words)

	Prime number
		In mathematics, a prime number, or prime for short, is a natural number larger than 1 that has as its only positive divisors (factors) 1 and itself.
		An important result is the fundamental theorem of arithmetic, which states that every natural number can be written as a product of primes, and in essentially only one way.
		In number theory itself, one talks of pseudoprimes, integers which, by virtue of having passed a certain test, are considered probable primes but are in fact composite (such as Carmichael numbers).
	www.ebroadcast.com.au /lookup/encyclopedia/pr/Prime.html (1702 words)

	11: Number theory
		Number theory is one of the oldest branches of pure mathematics, and one of the largest.
		Naturally there is significant overlap, and a single question from elementary number theory often requires tools from many branches of number theory.
		Questions in algebraic number theory often require tools of Galois theory; that material is mostly a part of 12: Field theory (particularly the subject of field extensions).
	www.math.niu.edu /~rusin/known-math/index/11-XX.html (2572 words)

	natural number
		The debate about whether zero should also be included as a natural number has been going on for hundreds of years, and there's no general agreement even today.
		To avoid confusion, 0, 1, 2, 3,..., are often referred to as non-negative integers or whole numbers, while 1, 2, 3,..., are called positive integers.
		An important property of the natural numbers is that they are well-ordered, in other words, every set of natural numbers has a smallest element.
	www.daviddarling.info /encyclopedia/N/natural_number.html (274 words)

	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 (194 words)

	RDEGRAAF.nl [Mathematics: Set Theory and Numbers] (Site not responding. Last check: 2007-10-21)
		In formal set theory, an ordinal number (sometimes simply called an "ordinal" for short) is one of the numbers in Georg Cantor's extension of the whole numbers.
		In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3,....
		A Gödel number is a unique number for a given statement that can formed as the product of successive primes raised to the power of the number corresponding to the individual symbols that comprise the sentence.
	www.rdegraaf.nl /index.asp?sND_ID=915157 (491 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/index.asp (3230 words)

	Ratio of natural numbers. Evolution of the real numbers.
		The natural number is the actual collection of units, /////, whether strokes, apples, letters, or the idea of units.
		The ratio of two natural numbers is their relationship with respect to relative size that we can express in words.
		Specifically, it is their relationship in which one number is a multiple of the other (so many times it), a part of it, or parts of it.
	www.themathpage.com /areal/ratio-natural-numbers.htm (1692 words)

	Could There Exist a Very Large Natural Number Physically Equal to Zero?
		The most basic concept of number is that of the natural numbers and the operations of arithmetic defined on them.
		The integers themselves are just natural numbers with an optional minus sign (or, if we want to be sophisticated, we can define each integer as the result of subtracting one natural number from another).
		These natural numbers can be shown to be the result of a series of arithmetic operations which only ever involve natural numbers and natural number operations.
	www.1729.com /blog/LargeNaturalNumberPhysicallyEqualToZero.html (1584 words)

	number - Wiktionary
		(countable) (mathematics) A member of one of several classes: natural numbers,integers, rational numbers, real numbers, complex numbers, quaternions.
		Number the baskets so that we can find them easily.
		I don't know how many books are in the library, but they must number in the thousands.
	en.wiktionary.org /wiki/number (268 words)

	Perkins School for the Blind: Monograph Number 1 - Natural Environments (Site not responding. Last check: 2007-10-21)
		Second, defining natural environments as necessitating the joint presence of children with or without disabilities or delays is limited and not consistent with research.” (Dunst 2001).
		Amend or clarify the Natural Environments language in Part C of Individuals with Disabilities Education Improvement Act (formerly IDEA) to include an array of service options within the regulations so that states that have categorically refused to allow these services will broaden their philosophy and practice.
		Part C has set the goal of full inclusion as the ultimate outcome for children with disabilities, but achieving that goal should not be limited to one service type and will require both creativity and flexibility in defining the array of service options for each child.
	www.perkins.org /section.php?id=220 (851 words)

	Earliest Known Uses of Some of the Words of Mathematics (N)
		The older nomenclature was that "natural number" meant "positive integer." This was unfortunate, because the set of non-negative integers is really much more "natural" in the sense that it has simpler properties.
		This method for allocating sample numbers to different strata was proposed by Jerzy Neyman, "On the two different aspects of the representative method; the method of stratified sampling and the method of purposive selection," J.
		Number line is found in January 1956 in "An exploratory approach to solving equations" by Max Beberman and Bruce E. Meserve in The Mathematics Teacher: "In an earlier paper we described a procedure by which students could 'solve' equations and inequalities using a number line.
	members.aol.com /jeff570/n.html (5389 words)

	BBC NEWS \| In Depth \| Natural disasters 'on the rise' (Site not responding. Last check: 2007-10-21)
		More and more people are being caught up in a growing number of natural disasters, a UN agency said on Friday.
		The International Strategy for Disaster Reduction said the increase in numbers vulnerable to natural shocks was due partly to global warming.
		There were 337 natural disasters reported in 2003, up from 261 in 1990.
	news.bbc.co.uk /2/low/in_depth/3666474.stm (341 words)

	Alternative Data Definitions for Natural Numbers (Site not responding. Last check: 2007-10-21)
		Note: The results of these expressions are large numbers, well beyond the native capacities of many other programming languages.
		The value of this selector expression belongs to the same class of data as the input and is thus a candidate for natural recursion.
		, which consumes a natural number and determines whether or not it is prime.
	www.htdp.org /2001-09-22/Book/node64.htm (724 words)

	Rational Number System
		Any number that can be written as a fraction where the numerator and denominator are integers.
		Any number that cannot be written as a fraction where the numerator and denominator are integers.
		Note: Since irrational numbers cannot be expressed as a fraction they form decimals that are neither repeating nor terminating.
	argyll.epsb.ca /jreed/math9/strand1/1101.htm (289 words)

	Program Files\Netscape\Communicator\Program\nshsalg\infinity
		which is, at best, just a subset of the set of all natural numbers.
		Thus, if we want to talk about the number of numbers in the set of all natural numbers we need to introduce a new number which is not a natural number.
		to be precisely the number of natural numbers.
	www.ii.uib.no /~wagner/hsalg/infinity.htm (257 words)

	Comp 210 Lab 4: More Lists, Natural Numbers
		As discussed in class, natural numbers are all the non-negative integers.
		Note that the natural numbers are structurally just like lists, if you ignore the elements of the lists.
		Develop a program which consumes a natural number and a symbol and returns a list of that many copies of the symbol.
	www.owlnet.rice.edu /~comp210/01fall/Labs/lab04 (646 words)

	[No title]
		In more detail: If P(x) is some open sentence about natural numbers in a variable x and if we know that there is some natural number n0 for which P(n0) is true then we can take the set T of all natural numbers for which the sentence P(X) is true.
		Theorem: If x > 1 is a natural number, and if x is NOT prime, then x can be written as the product of two natural numbers between it and 1 (that is: there exist natural numbers a and b such that 1 1.
		So we are assuming that there is some natural number greater than 1 which cannot be written as the product of primes.
	clem.mscd.edu /~evansell/MATH/ProductPrimes.doc (633 words)

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