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Topic: Real number

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Mathematical function

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Prime number

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	Reference.com/Encyclopedia/Extended real number line
		In mathematics, the affinely extended real number system is obtained from the real number system R by adding two elements: +∞ and −∞ (pronounced "positive infinity" and "negative infinity").
		The affinely extended real number system should be distinguished from the projectively extended real numbers by having two infinities, rather than one.
		This limiting behavior is similar to the limit of a function at a real number, except that there is no real number which x is approaching.
	www.reference.com /browse/wiki/Extended_real_number_line (995 words)

	Real number - Wikipedia, the free encyclopedia
		A real number may be defined as a complex number with zero imaginary part or thought of as any point on an infinitely long number line.
		The term "real number" is a retronym coined in response to "imaginary number".
		The non-existence of a subset of the reals with cardinality strictly between that of the integers and the reals is known as the continuum hypothesis.
	en.wikipedia.org /wiki/Real_number (2550 words)

	Number - Simple English Wikipedia
		Integers are all the positive numbers, all the negative numbers, and the number zero.
		Imaginary numbers are formed by real numbers multiplied by the number i.
		This number is the square root of minus one (-1).
	simple.wikipedia.org /wiki/Number (1192 words)

	Imaginary number - Wikipedia, the free encyclopedia
		In mathematics, an imaginary number (or purely imaginary number) is a complex number whose square is a negative real number.
		The number a is the real part of the complex number, and b is the imaginary part.
		Although Descartes originally used the term "imaginary number" to mean what is currently meant by the term "complex number", the term "imaginary number" today usually means a complex number with a real part equal to 0, that is, a number of the form bi.
	en.wikipedia.org /wiki/Imaginary_number (944 words)

	Math Forum: Ask Dr. Math FAQ: Imaginary Numbers
		Contrary to what some people might tell you, imaginary numbers are not numbers that only exist in the brains of weird people.
		Imaginary numbers are numbers that can be written as a real number times i.
		So the real numbers are the numbers that you probably already know: they're the ones on the number line.
	www.mathforum.org /dr.math/faq/faq.imag.num.html (340 words)

	Schloss Dagstuhl : Seminar Homepage
		Real numbers are objects containing an infinite amount of information.
		There are many approaches that deal with the reliable implementation of real number algorithms from a practical point of view.
		In computational geometry the special problem of implementing real number algorithms reliably is complicated by the interplay of numerical predicates and hidden dependencies between them that arise from geometry theorems that may not be known.
	www.dagstuhl.de /06021 (672 words)

	Inequalities. Set Notation etc.
		A bigger number will always be found to the right of a smaller number.
		The number -2 is excluded from the set, so you see an "empty bubble"; the number 5 is included in the set, so the bubble at 5 is "filled in."
		The set does not need to be "connected." The following graph depicts all real numbers which are either greater than 2 or strictly between -1 and 1.
	www.sosmath.com /algebra/inequalities/ineq02/ineq02.html (657 words)

	Number Types
		The next type is the "rational", or fractional, numbers, which are technically regarded as ratios (divisions) of integers.
		The commonest question I hear regarding number types is something along the lines of "Is a real number irrational, or is an irrational number real, or neither...
		Except for the section where you have to classify numbers according to type, you really won't need to be terribly familiar with this hierarchy.
	www.purplemath.com /modules/numtypes.htm (775 words)

	Ms. Magazine \| The Real Number on Social Security
		Private accounts would be a disaster, writes a woman from the generation Bush claims he’s helping — but something else in the system really does need fixing.
		What he has talked about, endlessly, is his plan to add private investment accounts to Social Security, promising high stock-market returns and individual autonomy.
		Bush has camouflaged the real impact of this plan, though — such as the inconvenient fact that private accounts don’t supplement but replace a percentage of traditional benefits — and has, perhaps willfully, confounded the public.
	www.msmagazine.com /summer2005/socialsecurity.asp (1495 words)

	616 vs. 666: Which Is the Real Number of the Beast? (Site not responding. Last check: )
		You may have seen in the news recently that a fragment of the "oldest NT manuscript" was found to say in Revelation 13:18 that the number of the beast was 616 instead of 666.
		A newly discovered fragment of the oldest surviving copy of the New Testament indicates that, as far as the Antichrist goes, theologians, scholars, heavy metal groups, and television evangelists have got the wrong number.
		There is such a man. Prince Charles of Wales' heraldic achievement (coat-of-arms) literally consists of the very beasts described in Rev 13 and Dan 7, he is a Prince (Dan 9:27) and he is from the old Roman Empire that destroyed the Temple (Dan 9:27).
	www.escapeallthesethings.com /666-616-number-mark-of-the-beast.htm (1512 words)

	number. The Columbia Encyclopedia, Sixth Edition. 2001-05
		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.
		The complex numbers are in a one-to-one correspondence with the points of a plane, with one axis defining the real parts of the numbers and one axis defining the imaginary parts.
	www.bartleby.com /65/nu/number.html (513 words)

	Real number : Real
		Real numbers may be expressed by decimal fractions, such as 324.823211247...; it is recursive[?] if the digits can be specified by a recursive algorithm.
		It's impossible to explicitly specify a non-recursive number; the Russian school[?] of constructivism assumes that all real numbers are recursive.
		Occasionally, formal elements +∞ and -∞ are added to the reals to form the extended real number line, a compact space which isn't a field anymore but retains many of the properties of the real numbers.
	www.wordlookup.net /re/real.html (2476 words)

	real number
		Real numbers stand in one-to-one correspondence with the points on a continuous line, known as the real number line, that stretches from zero to infinity in both directions.
		The name "real number" is a retronym, coined by René Descartes in response to the concept of imaginary numbers.
		Number systems that are even more general that the real numbers include the complex numbers and, of much more recent discovery, hyperreal numbers and surreal numbers.
	www.daviddarling.info /encyclopedia/R/real_number.html (178 words)

	PlanetMath: real number
		There are several equivalent definitions of real number, all in common use.
		The real numbers can also be defined as the unique (up to isomorphism) ordered field satisfying the least upper bound property, after one has proved that such a field exists and is unique up to isomorphism.
		This is version 17 of real number, born on 2001-10-21, modified 2005-08-15.
	planetmath.org /encyclopedia/MathbbR.html (861 words)

	Real number - Simple English Wikipedia
		A real number is a rational or irrational number.
		Usually when people say "number" they mean "real number".
		There are also numbers which are not real: complex numbers.
	simple.wikipedia.org /wiki/Real_number (302 words)

	Real numbers 2
		Though Cauchy understood that a real number could be obtained as the limit of rationals, he did not develop his insight into a definition of real numbers or a detailed description of the properties of real numbers.
		His definition of a real number was made in terms of convergent sequences of rational numbers and is explained in [Casopis Pest.
		Similarly Cantor realised that if he wants the line to represent the real numbers then he has to introduce an axiom to recover the connection between the way the real numbers are now being defined and the old concept of measurement.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Real_numbers_2.html (2626 words)

	What's a number?
		Thus the set R of all real numbers is the union of two sets - algebraic and transcendental.
		The rest of the complex numbers could also be defined by adding this new number i to the set of reals and postulating that usual arithmetic operations (addition, subtraction, multiplication) apply to the expanded set and all the laws known to hold for these operations hold for the new set as well.
		This is an equation of a real (i.e.
	www.cut-the-knot.org /do_you_know/numbers.shtml (3546 words)

	real number from FOLDOC (Site not responding. Last check: )
		The integers ("counting numbers") are real numbers with no fractional part and real numbers ("measuring numbers") are complex numbers with no imaginary part.
		The real numbers are the minimal topologically closed field containing the rational field.
		Indeed, there is a natural embedding of the rationals in the reals (via, for any rational, the sequence which takes no other value than that rational) which suffices, when extended via continuity, to import most of the algebraic properties of the rationals to the reals.
	ftp.sunet.se /foldoc/foldoc.cgi?real+numbers (328 words)

	Real (JScience v3.1 API)
		The decimal representations of real instances are indicative of their precision as only exact digits are written out.
		Returns the square root of this real number, the more accurate is this real number, the more accurate the square root.
		the real number corresponding to the specified integer with the specified number of decimal zero.
	jscience.org /api/org/jscience/mathematics/numbers/Real.html (1017 words)

	The Real Number System (Site not responding. Last check: )
		The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, like how many sheep a farmer owns.
		Note that the negative sign in front of a number is part of the symbol for that number: The symbol “–3” is one object—it stands for “negative three,” the name of the number that is three units less than zero.
		Any number that represents an amount of something, such as a weight, a volume, or the distance between two points, will always be a real number.
	www.jamesbrennan.org /algebra/numbers/real_number_system.htm (1567 words)

	real number - Anarchopedia
		Informally, the "real numbers" are the rational numbers with all the holes plugged.
		If we view the rational numbers as being contained in the set of cuts, via the correspondence $q \leftrightarrow \Gamma(q)$ , then the set of cuts must therefore be a proper superset of the rational numbers.
		In our model for the real numbers, the least upper bound of such a set is the cut itself.
	meta.anarchopedia.org /Real_number (1187 words)

	Real numbers 3
		Some of the intuitive difficulties that began to be felt revolved around the fact that the real numbers were not countable, that is, they could not be put in 1-1 correspondence with the natural numbers.
		Cantor proved that the real numbers were not countable in 1874.
		Now the real number r cannot be described in English, since it differs by construction from every real number which can be described in English.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Real_numbers_3.html (2182 words)

	Wikinfo \| Real number
		Mathematicians use the symbol R (or alternatively, BbbR, the letter "R" in flboard bold) to represent the set of all real numbers.
		Occasionally, formal elements +∞ and -∞ are added to the reals to form the extended real number line, a compact space which is not a field anymore but retains many of the properties of the real numbers.
		Images, some of which are used under the doctrine of Fair use or used with permission, may not be available.
	www.wikinfo.org /wiki.php?title=Real_number (2064 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.
		The real numbers have many properties that are both useful and surprising, as you will discover in your continued study.
	www.mathacademy.com /pr/minitext/number/index.asp (3230 words)

	Math 1010 on-line - The Real Number Line
		A positive number x corresponds to a point x units away from the origin to the right, and a negative number -x corresponds to a point on the line x units away from the origin to the left.
		We said that the number corresponds to a point on the real number line, but actually there is no useful distinction between a real number and its corresponding point on the real number line.
		Hence we may also say that a real number is on the real line, and a point on the real number line is a real number.
	www.math.utah.edu /online/1010/line (488 words)

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