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Topic: Negative number

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	Negative and non-negative numbers - Wikipedia, the free encyclopedia
		Negative integers can be regarded as an extension of the natural numbers, such that the equation x − y = z has a meaningful solution for all values of x and y.
		Negative numbers are useful to describe values on a scale that goes below zero, such as temperature, and also in bookkeeping where they can be used to represent debts.
		This is the earliest known mention of negative numbers in the East, the first indication in a western work was in the 3rd century in Greece.
	en.wikipedia.org /wiki/Non-negative (1212 words)

	Kids.net.au - Encyclopedia Real number - (Site not responding. Last check: 2007-11-07)
		Real numbers may be rational or irrational; algebraic or transcendental; and positive, negative, or zero.
		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.
		Negative numbers began to be generally accepted in the 1600s and were invented by Muslim mathematicians.
	www.kids.net.au /encyclopedia-wiki/re/Real_number (2268 words)

	Positive and negative numbers
		The number line is a line labeled with positive and negative numbers in increasing order from left to right, that extends in both directions.
		Number coordinates are pairs of numbers that are used to determine points in a grid, relative to a special point called the origin.
		The reciprocal of a positive or negative fraction is obtained by switching its numerator and denominator, the sign of the new fraction remains the same.
	www.mathleague.com /help/posandneg/posandneg.htm (1681 words)

	Integers
		Negative integers are all the opposites of these whole numbers: -1, -2, -3, -4, -5, ….
		The number of units a number is from zero on the number line.
		If the number of negative integers counted in step 1 is even, the product is just the product from step 2, if the number of negative integers is odd, the product is the opposite of the product in step 2 (give the product in step 2 a negative sign).
	www.mathleague.com /help/integers/integers.htm (1525 words)

	Negative and non-negative numbers - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		Nevertheless, Ancient India is then credited with the earliest known use and legitimization of negative numbers in mathematics after the era of the Indus Valley peoples, in Brahmagupta's BrahmaSphuta-Sidd'hanta [628], an Indian mathematical text.
		In Brahmagupta's work, it appears as if negative numbers evolved from a need to represent negative asset or debts.
		European mathematicians, for the most part, resisted the concept of negative numbers until the 17th century.
	www.sevenhills.us /project/wikipedia/index.php/Negative_number (1127 words)

	MSN Encarta - Search Results - Negative Number
		We can most easily visualize negative numbers by considering the familiar numbers of arithmetic, the positive integers, arranged in a line and...
		Imaginary Numbers, numbers formed by multiplying a real number times i, where i is the square root of minus 1.
		Determine which is greater.Graph the point that corresponds to the positive number to the right of zero, and the point that corresponds to the negative number to the left of zero.
	encarta.msn.com /Negative_Number.html (181 words)

	MathSteps: Grade 5: Negative Numbers: What Is It?
		Mathematicians define negative numbers as the opposites of positive numbers, since they are on the opposite side of zero from the positive numbers on a number line.
		Similarly, the opposites of the negative numbers are the positive numbers.
		Negative numbers are always written with a negative sign, but positive numbers may be written without a positive sign.
	www.eduplace.com /math/mathsteps/5/a (362 words)

	Negative Number (Site not responding. Last check: 2007-11-07)
		The origin divides the number line into two regions: the region to the right of the origin is the positive side; the region to the left of the origin is the negative side.
		The number is known as the coordinate of the point; the point is known as the graph of the number.
		For instance, the number -5 is graphed and labeled as the point P. Point P is located 5 units from the left of the origin O. -5 is the coordinate of P; P is the graph of -5.
	www.gomath.com /htdocs/lesson/negative_lesson1.htm (215 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-07)
		The actual change means something, but dividing it by a number that may be zero or of the opposite sign does not convey any meaningful information, because the amount by which a profit changes is not proportional to its previous value.
		Negative divided by positive, or positive divided by negative, is negative; negative divided by negative is positive.
		You'll need to explain that, if the target is negative, then a positive percentage greater than 100 means you did even worse than you expected; a positive percentage less than 100 means you didn't do as badly as you expected; and a negative percentage means you had a profit after all.
	mathforum.org /library/drmath/view/55720.html (1537 words)

	Real number - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-11-07)
		Writing them as decimal fractions (which are rational numbers that could be written as ratios, with an explicit denominator) is not only more compact, but to some extent expresses the sense of an underlying real number.
		Real numbers could be constructed as the topological completion of rational numbers.
		Self-adjoint operatorss on a Hilbert space (for example, self-adjoint square complex matrices) generalize the reals in many respects: they can be ordered (though not totally ordered), they are complete, all their eigenvalues are real and they form a real associative algebra.
	encyclopedia.learnthis.info /r/re/real_number.html (1932 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-07)
		Negative solutions to problems were for centuries called "false" because they can't be found in the real world.
		The basic ideas of negative numbers were recognized in some form as early as Diophantus (third century A.D.), and were explicitly discussed by Brahmagupta (seventh century); Fibonacci, about 1200, allowed negative solutions in financial problems where they could be interpreted as a loss rather than a gain.
		As you can see, it was just a gradual recognition of the value of negative numbers that led them from grudging acceptance to full equality with positive numbers.
	mathforum.org /library/drmath/view/52593.html (297 words)

	The Real Number System (Site not responding. Last check: 2007-11-07)
		It took longer for the idea of negative numbers to be accepted, but eventually they came to be seen as something we could call “numbers.” The expanded set of numbers that we get by including negative versions of the counting numbers is called the integers.
		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.
		Negative numbers represent distances to the left of zero, and positive numbers are distances to the right.
	www.jamesbrennan.org /algebra/numbers/real_number_system.htm (1567 words)

	MathSteps: Grade 6: Negative Numbers: What Is It?
		A positive number means a move to the right on the number line, while a negative number means a move to the left.
		The rules for operations with negative numbers may seem arbitrary and mysterious – but they are not as arbitrary as they seem.
		When subtracting with negative numbers on a number line, the subtraction sign means to go in the opposite direction of the directed distance that follows.
	www.eduplace.com /math/mathsteps/6/b (588 words)

	SparkNotes: Integers and Rationals: Operations with Negative Numbers
		On the number line, moving to the left is equivalent to subtracting from a number, and moving to the right is equivalent to adding to a nu mber.
		Multiply the numbers with their signs removed and make this result positive or negative according to the total number of negative signs.
		Divide the numbers with their signs removed, and make this result positive or negative according to the total number of negative signs (positive if the total number of negative signs is even, negative if it is odd).
	www.sparknotes.com /math/prealgebra/integersandrationals/section3.rhtml (646 words)

	CUNYMath: A Multilingual Glossary of Math Terms for ESL Students
		An irrational number is a number that cannot be expressed as a fraction.
		The opposite of a number is the number with the opposite sign.
		A prime number is a natural number that has only one and itself as factors.
	www.cunymath.cuny.edu /students/glossary/n-p.html (362 words)

	Log of Negative Number (Site not responding. Last check: 2007-11-07)
		But for example the natural log of -1 (ln(-1)) is plus or minus i * pi, where i is the square root of -1, and pi, is your old friend from circles and diameters.
		Ten raised to an imaginary number can be negative, so the log of a negative number is imaginary.
		So long as you use only real numbers that represent real amounts, the log of a negative number is undefined.
	www.newton.dep.anl.gov /askasci/math99/math99180.htm (399 words)

	Negative Number (Site not responding. Last check: 2007-11-07)
		The sum or difference between a negative number and a negative number, or between a negative number and a positive number can be demonstrated using a number line.
		A negative sign indicates moving the coordinate to the left.
		Other methods for adding (or subtracting) negative and positive numbers are the rules for addition.
	www.gomath.com /htdocs/lesson/negative_lesson2.htm (194 words)

	Negative Numbers (Site not responding. Last check: 2007-11-07)
		The ancient Chinese calculated with colored rods, red for positive quantities and fl for negative (just the opposite of our accounting practices today) but, like their European counter- parts, they would not accept a negative number as a solution of a problem or equation.
		As recently as the 1500s there were European mathematicians who argued against the "existence" of negative numbers by saying Zero signifies "nothing", and it's impossible for anything to be less than nothing.
		He even gave the rules for arithmetic, e.g., "a negative number divided by a negative number is a positive number", and so on.
	www.mathpages.com /home/kmath298.htm (343 words)

	Math Forum: Ask Dr. Math FAQ: Negative Times a Negative
		People have suggested many ways of picturing what is going on when a negative number is multiplied by a negative number.
		Negative steps require you to face the negative end of the line before you start walking and negative step sizes are backward (i.e., heel first) steps.
		Suppose you're standing on a road, and you measure mileage to the east as positive, and to the west as negative.
	mathforum.org /dr.math/faq/faq.negxneg.html (1005 words)

	Question Corner -- Why is the Product of Negative Numbers Positive?
		This is in fact the reason why the negative numbers were introduced: so that each positive number would have an additive inverse.
		The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.
		This is a comment on your answer to the question: "Why is a negative number times a negative number a positive number?" As a volunteer teacher for a pre-algebra class of sixth graders, I addressed the same question with the following practical demonstration.
	www.math.toronto.edu /mathnet/questionCorner/minustimesaminus.html (928 words)

	Complex Numbers Lesson - I
		Now, however, you can take the square root of a negative number, but it involves using a new number to do it.
		This new number was invented (discovered?) around the time of the Reformation.
		At this time, nobody believed that any "real world" use would be found for this new number, other than easing the computations involved in solving certain equations, so the new number was viewed as being a pretend number invented for convenience sake.
	www.purplemath.com /modules/complex.htm (500 words)

	Minus Zero
		In ten's complement, if the number is negative we subtract its magnitude from the number one greater than our register size and enter the result.
		The oddity of a negative number with no positive counterpart is also gone; the nine's complement of the largest positive number, 4999 is 5000, which represents -4999 just as you'd expect.
		In summary, by admitting the added complexity of end-around carry, we have obtained a way of representing negative numbers which is symmetric, in which power-of-two division can be done by shifting for all numbers, and where negating a number and inverting all its bits are one and the same thing.
	www.fourmilab.ch /documents/univac/minuszero.html (2934 words)

	Biology/Chemistry
		The students will learn how to add and subtract using the number line with positive and negative numbers.
		0, and the negative numbers are to the left of zero.
		When you move in the negative direction on the number line, it does not mean that you are going backwards, but simply that you have changed direction.
	www.iit.edu /~smile/phma0100.htm (496 words)

	Negative Numbers Review - I
		If you are adding a negative, this is pretty much the same as subtracting a positive, if you view "adding a negative" as adding to the left.
		You know now that the answer will be negative, because you're subtracting a bigger number than you started with (nine is bigger than five).
		Adding two negative numbers is easy: you're just adding two "negative" arrows, so it's just the backwards of "regular" addition.
	www.purplemath.com /modules/negative.htm (955 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-07)
		Dear Confused, (This sounds like an advice column...) Here are your rules for negative and positive numbers: ADDITION: If the signs are the same then you add the two numbers and keep the sign.
		For example, 2^2 = 22 (The 2^2 means 2 raised to the power two) 3^4 = 3333 So (-3)^2 = (-3)(-3) Now just use the rules of multiplying two negative* numbers together to get the answer.
		If you're cubing a number, it's just as if you've multiplied it together three times.
	mathforum.org /library/drmath/view/57866.html (481 words)

	[xmlsec] Problem with some cert which has a negative serial number
		I think the question is when getting a negative serial number, we treat it as positive integer and convert it to positive decimal string.
		So while convert the decimal string back, we treat it as positive instead of negative, so we get a wrong serial number.
		What we need is convert a negative big number into a decial string with '-' sign, I think it is also the stand form of XML integer representation.
	www.aleksey.com /pipermail/xmlsec/2005/002516.html (622 words)

	Integers (Site not responding. Last check: 2007-11-07)
		List three words that would represent a negative number and three words that would represent a positive number.
		The integer will be plotted on the number line using a red mark and its opposite will be plotted in yellow.
		The only number the teacher should place on the number line is zero and the appropriate tick marks so students can place the other numbers.
	www.richlandclicks.org /teacher/connections/grade7/integers.htm (721 words)

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