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Topic: Negative and nonnegative numbers

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complex number

natural number

prime number

atomic number

number theory

cardinal number

ordinal number

rational number

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	Negative and non-negative numbers - Wikipedia, the free encyclopedia
		A negative number is a number that is less than zero, such as −3.
		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.
		He also finds negative solutions to quadratic equations and gives rules regarding operations involving negative numbers and zero, such as "a debt cut off from nothingness becomes a credit, a credit cut off from nothingness becomes a debt." He called positive numbers "fortunes", zero a "cipher", and negative numbers a "debt".
	en.wikipedia.org /wiki/Negative_and_non-negative_numbers (1545 words)

	Negative and non-negative numbers
		A signed number is a number which has either a positive or negative sign (or in the case of zero, neither).
		On a computer, the sign of a number (whether it is positive or negative) is usually expressed using the left-most bit.
		The most common system for representing negative integers in a fixed set of bits is termed "two's complement", in which negative numbers are represented by complementing the absolute value and then adding one to the value as if it were unsigned.
	www.ebroadcast.com.au /lookup/encyclopedia/un/Unsigned.html (818 words)

	Math 10 Pure - Real Numbers
		These numbers have been studied for thousands of years and were the first numbers used by mathematicians.
		Note that whereas the absolute value of a nonnegative number is the number itself, the absolute value of a negative number is positive.
		For any two numbers on the number line, the one to the left is said to be less than, or smaller than, the one to the right.
	argyll.epsb.ca /lburns/real_numbers_1.1.html (1081 words)

	Negative (Site not responding. Last check: 2007-10-20)
		Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e.,
		The concept of negative numbers is one that took millennia to become firmly embedded in mathematics.
		The acceptance of the square roots of negative numbers (i.e., so-called complex numbers) as useful abstract quantities took longer still.
	users.skynet.be /fa956617/math/topics/Negative.html (140 words)

	Floating-Point Numbers
		For a negative number, we may set the sign bit of the floating-point word and negate the number to be encoded, leaving only nonnegative numbers to be considered.
		The basic idea of floating point encoding of a binary number is to normalize the number by shifting the bits either left or right until the shifted result lies between 1/2 and 1.
		The normalized number between 1/2 and 1 is called the significand, so called because it holds all the ``significant bits'' of the number.
	ccrma-www.stanford.edu /~jos/mdft/Floating_Point_Numbers.html (509 words)

	Whole number - Wikipedia, the free encyclopedia
		The whole numbers are the nonnegative integers (0, 1, 2, 3,...)
		The set of all whole numbers is represented by the symbol
		Simmons, B. MathWords presents the whole numbers as "0, 1, 2, 3,..." in a Venn diagram of common numeric domains.
	en.wikipedia.org /wiki/Whole_number (213 words)

	Roots and Radical Expressions
		The principal square root of a non-negative number is its nonnegative square root.
		Since m could be any real number value, positive or negative, and the symbol used in the principal square root, we should indicate the absolute value of m to ensure the result is non-negative.
		The cube root of a negative number is negative.
	www.jcoffman.com /Algebra2/ch7_1.htm (529 words)

	Sample Questions: GRE Verbal and Quantitative Section
		Numbers are to be used as exact numbers, even though in some contexts they are likely to have been rounded.
		For any two numbers on the number line, the number on the left is less than the number on the right; for example, -4 is to the left of -3, which is to the left of 0.
		The number of degrees of arc in a circle is 360.
	www.ets.org /vgn-ext-templating/v/?vgnextoid=ef852d3631df4010VgnVCM10000022f95190RCRD&vgnextchannel=06a7e3b5f64f4010VgnVCM10000022f95190RCRD (2606 words)

	Number Theory - Numericana
		Recall that a number is divisible by 3 or 9 iff (if and only if) the sum of its digits is. It is divisible by 11 iff the difference between the sum of its odd digits (units, hundreds, etc.) and the sum of its even digits (tens, thousands, etc.) is so divisible.
		Since the number 9N divides the number which consists of P nines followed by a certain number J of zeroes, N divides the number consisting of P ones followed by J zeroes, and also the integer composed of P sevens followed by J zeroes.
		The next two numbers in the list, the 13th and 14th Mersenne primes, are much larger (corresponding to n=521 and n=607) and were both discovered the same day (January 30, 1952, around 22:00 PST and shortly before midnight) by Raphael Mitchel Robinson (1911-1995), at the dawn of the computer age.
	home.att.net /~numericana/answer/numbers.htm (7587 words)

	Numbers and Functions as Continued Fractions - Numericana
		The first entry in the table below (the so-called Golden Number) is the continued fraction with the slowest convergence (the lower the partial quotients, the slower the convergence).
		The usual probability measure (Lebesgue measure) for sets of numbers between 0 and 1 thus translates into statistical properties for their partial quotients, which were investigated by the Russian mathematician A.Ya.
		For negative numbers, we take the reciprocal of the opposite [which is positive] and obtain the result as the opposite of that.
	home.att.net /~numericana/answer/fractions.htm (3600 words)

	11 Numbers, +ve or -ve
		The addition of a negative number and the subtraction of a positive number corresponds to a downward movement.
		The subtraction of a negative number in the first instance is undefined.
		Note that multiplication of a number a by a whole number n, can be viewed as the result of the addition of a to itself, a whole number n times.
	whyslopes.com /etc/MathCurriculumNotes/ch11j_Signed_Numbers.html (655 words)

	Integer Arithmetic (Site not responding. Last check: 2007-10-20)
		A method of representing numbers that avoids this problem and simplifies the arithmetic and circuitry is called two's complement notation.
		For negative numbers, however, the sequence of bits after the most significant bit of 1 is not the magnitude in base 2.
		In general, the two's complement of the two's complement is the original number; just as taking the negative of a negative is positive.
	www.wofford.edu /ecs/scientificprogramming/Error/IntegerArithmetic/material.htm (1649 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-20)
		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.
		Properly, the modulus operator a mod b should be mathematically defined as the number in the range [0,b) that is congruent to a, as stated here: http://mathworld.wolfram.com/ModulusCongruence.html In many computer languages (such as FORTRAN or Mathematica), the common residue of b (mod m) is written mod(b,m) (FORTRAN) or Mod[b,m] (Mathematica).
		Actually, its behavior for negative numbers is not even defined officially; like many things in C, it's left to be processor-dependent because C does not define how a processor should handle integer division.
	mathforum.org /library/drmath/view/52343.html (2075 words)

	Complex numbers
		A complex number is the sum of a real number and a real multiple of the ``imaginary unit'' i, which is conventionally interpreted as the principal square root of -1.
		The complex numbers that can be represented exactly form an irregular lattice of points on the plane, each serving as the representative for the points in a rectangular region surrounding it.
		Most of the arithmetic functions on complex numbers begin by coercing their operands to whichever form, rectangular or polar, allows the operation to be coded more easily.
	www.math.grin.edu /~stone/courses/fundamentals/complex-numbers.html (2008 words)

	10.1: Radical Expressions (Site not responding. Last check: 2007-10-20)
		Negative numbers do not have real number square roots; they have roots which are imaginary (imaginary numbers).
		Principal Square Root: A number is a principal square root if it is the nonnegative square root of a nonnegative number.
		The radicand was negative, the index was odd, and the negative root was indicated....
	www.mtsu.edu /~mhiggs/101.html (463 words)

	Cholesky Matrix
		If we think of matrices as multi-dimensional generalizations of numbers, we may draw useful analogies between numbers and matrices.
		It is useful to think of positive definite matrices as analogous to positive numbers and positive semidefinite matrices as analogous to nonnegative numbers.
		complex number A number of the form a + bi, where a and b are real, and i is the imaginary square root of the number —1.
	www.riskglossary.com /articles/cholesky_factorization.htm (993 words)

	Complex No Intro - Vector and Complex Numbers:
		The angle of a purely imaginary complex number z = a+ib = 0+ib = (0,b) is 90 degrees or 270 degrees (modulo 360 degrees), depending on the sign of the imaginary part b.
		With this practice, the real numbers can be regarded as a subset of the complex numbers; and the real number line can be identified with the horizontal axis of the plane.
		Since the angle 180 degrees is associated with -1, and the angles 0 and 360 degrees are both associated with the number +1, the polar coordinate definition of multiplication of points in the plane agrees with (or yields) the law of signs for the multiplication of positive and negative numbers.
	whyslopes.com /etc/ComplexNumbers/complex.html (3307 words)

	Math Forum Discussions
		(The number q might well have been called "THE square root of p".) As used now and imbedded in calculators, sqrt is a function with source and target both being the non-negative real numbers so that sqrt(p) is q, and with the addition of 0 so that sqrt(0) is 0.
		Well, people grew confortable with using negative numbers and started to look for all the solutions to equations -- often the equation was f(t)=0 where f(t) was a polynomial.
		And when p is nonnegative, we assume that t is some numerical expression such that abs(t)=p and then ask what we may properly deduce from that.
	mathforum.org /kb/thread.jspa?threadID=1211034&messageID=3922880 (588 words)

	9_1classnotes
		A square root is a number that when squared is equal to a given number or to a given radicand in a radical expression.
		The principal and/or the negative square root of a negative number are not found in the set of real numbers.
		A cube root is a number that when cubed is equal to a given number or to a given radicand in a radical expression.
	mtsu32.mtsu.edu:11237 /9_1classnotes.htm (538 words)

	XEmacs Lisp Reference Manual - 4. Numbers (Site not responding. Last check: 2007-10-20)
		The number prefixes `#b', `#o', and `#x' are supported to represent numbers in binary, octal, and hexadecimal notation (or radix).
		Floating point numbers are numbers with fractional parts, such as -4.5, 0.0, or 2.71828.
		For negative arguments, the remainder is in principle machine-dependent since the quotient is; but in practice, all known machines behave alike.
	www.cse.ohio-state.edu /~cmcurtin/xemacs-doc/lispref/lispref_4.html (2818 words)

	Fixed Point Arithmetic
		To represent negative values, naturally we need a different interpretation of binary words, and we introduce the two's complement representation and corresponding operations to implement arithmetic on the numbers represented in the two's complement format.
		In C6211, it is easiest to handle Q-15 numbers represented by each 16 bit binary word, because the multiplication of two Q-15 numbers results in a Q-30 number that can still be stored in a 32-bit wide register of C6211.
		The addition of two binary numbers is computed in the same way as we compute the sum of two decimal numbers.
	cnx.org /content/m11054/latest (1847 words)

	Z-property of natural numbers
		In fact, it follows from Table 1 that the sum B of Fibonacci numbers with the binary coefficients given by (7) and the sum A of Lucas numbers with the binary coefficients given by (6) are integer numbers always.
		-code (1) is the representation of the number N as the sum of the golden ratio powers, the F-code (11) is the representation of the same number N as the sum of the Fibonacci numbers and the L-code (14) is the representation of the same number N as the sum of the Lucas numbers.
		We can see that the latter is separated by the comma into two parts namely the left part consisting of the digits with the nonnegative indices and the right part consisting of the digits with the negative indices.
	www.goldenmuseum.com /1106Zproperty_engl.html (992 words)

	SparkNotes: SAT Math Level 2: Domain and Range (Site not responding. Last check: 2007-10-20)
		It is common for a domain to include only positive numbers, only negative numbers, or even all numbers except one or two points.
		A negative number has no square root defined in the real number system—f(x) and is undefined for all x < 0.
		A function is undefined for all values of x that causes a negative number to be the radicand of an even root.
	www.sparknotes.com /testprep/books/sat2/math2c/chapter10section5.rhtml (1509 words)

	Elementary Functions Lecture Notes, 09/08/00 (Site not responding. Last check: 2007-10-20)
		Definition: Let a be a real number, and let n be an integer greater than or equal to 2.
		In the following, let a and b be real numbers, let m and n be integers greater than or equal to 2.
		Definition: Let a be a real number, and let m and n be integers with no common factors and with n greater than or equal to 2.
	www.assumption.edu /Alfano/MAT114-FA00/Notes/090800.html (734 words)

	XEmacs Lisp Reference Manual - Random Numbers (Site not responding. Last check: 2007-10-20)
		A series of pseudo-random numbers is generated in a deterministic fashion.
		The numbers are not truly random, but they have certain properties that mimic a random series.
		In XEmacs, pseudo-random numbers are generated from a "seed" number.
	www.tau.ac.il /cc/pages/docs/xemacs/lispref_84.html (236 words)

	Givat Ram FAQ: mathcondarg (Site not responding. Last check: 2007-10-20)
		This may be either (strict) Positive, or (strict) Negative, or NonNegative, or NonPositive.
		The following Mathematica codes define a function that computes the number of prime numbers at most equal to a given natural number n at least equal to 2.
		On the other hand, one can see that there are 25 prime numbers between 2 and 100, including 2.
	shum.cc.huji.ac.il /cc/FAQ/mathcondarg.html (367 words)

	[No title]
		Use the terms that follow to identify each of the sets set of natural numbers, set of whole numbers, set of integers, set of rational numbers, set of irrational numbers, set of real numbers, set of prime numbers { 1, 2, 3, 4, 5,...
		Use the terms that follow to identify each of the sets set of natural numbers, set of whole numbers, set of integers, set of rational numbers, set of irrational numbers, set of real numbers, set of prime numbers { 0, 1, 2, 3, 4, 5,...
		Give me an example of a) an integer that is not a whole number ______________ b) a rational number that is not an integer _______ 2.
	www.angelo.edu /faculty/jmontema/1311-notes1.doc (2485 words)

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