−1

picture info	−1 In mathematics, −1 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0. In mathematics Algebraic properties Multiplying a number by −1 is equivalent to changing the sign of the number – that is, for any we have . This can be proved using the distributive law and the axiom that 1 is the multiplicative identity: :. Here we have used the fact that any number times 0 equals 0, which follows by cancellation from the equation :. In other words, :, so is the additive inverse of , i.e. , as was to be shown. The square of −1 (that is −1 multiplied by −1) equals 1. As a consequence, a product of two negative numbers is positive. For an algebraic proof of this result, start with the equation :. The first equality follows from the above result, and the second follows from the definition of −1 as addi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
	Two's Complement Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. Two's complement uses the binary digit with the ''greatest'' value as the ''sign'' to indicate whether the binary number is positive or negative; when the most significant bit is ''1'' the number is signed as negative and when the most significant bit is ''0'' the number is signed as positive. As a result, non-negative numbers are represented as themselves: 6 is 0110, zero is 0000, and −6 is 1010 (the result of applying the bitwise NOT operator to 6 and adding 1). However, while the number of binary bits is fixed throughout a computation it is otherwise arbitrary. Unlike the ones' complement scheme, the two's complement scheme has only one representation for zero. Furthermore, arithmetic implementations can be used on signed as well as unsigned integers and differ only in the integer overflow situations. Proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
	Signed Magnitude In computing, signed number representations are required to encode negative numbers in binary number systems. In mathematics, negative numbers in any base are represented by prefixing them with a minus sign ("−"). However, in RAM or CPU registers, numbers are represented only as sequences of bits, without extra symbols. The four best-known methods of extending the binary numeral system to represent signed numbers are: sign–magnitude, ones' complement, two's complement, and offset binary. Some of the alternative methods use implicit instead of explicit signs, such as negative binary, using the base −2. Corresponding methods can be devised for other bases, whether positive, negative, fractional, or other elaborations on such themes. There is no definitive criterion by which any of the representations is universally superior. For integers, the representation used in most current computing devices is two's complement, although the Unisys ClearPath Dorado series mainfr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
picture info	Chinese Numerals Chinese numerals are words and characters used to denote numbers in written Chinese. Today, speakers of Chinese languages use three written numeral systems: the system of Arabic numerals used worldwide, and two indigenous systems. The more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These may be shared with other languages of the Chinese cultural sphere such as Korean, Japanese, and Vietnamese. Most people and institutions in China primarily use the Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on cheques, banknotes, some ceremonial occasions, some boxes, and on commercials. The other indigenous system consists of the Suzhou numerals, or ''huama'', a positional system, the only surviving form of the rod numerals. These were once used by Chinese mathematicians, and later by merchants in Chinese markets, such as those in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
picture info	Integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
picture info	Complex Number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
picture info	Imaginary Unit The imaginary unit or unit imaginary number () is a mathematical constant that is a solution to the quadratic equation Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of in a complex number is Imaginary numbers are an important mathematical concept; they extend the real number system \mathbb to the complex number system \mathbb, in which at least one Root of a function, root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term ''imaginary'' is used because there is no real number having a negative square (algebra), square. There are two complex square roots of and , just as there are two complex square roots of every real number other than zero (which has one multiple root, double square root). In contexts in which use of the letter is ambiguous or problematic, the le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]
picture info	Sign (mathematics) In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign. In some contexts, it makes sense to distinguish between a positive and a negative zero. In mathematics and physics, the phrase "change of sign" is associated with exchanging an object for its additive inverse (multiplication with −1, negation), an operation which is not restricted to real numbers. It applies among other objects to vectors, matrices, and complex numbers, which are not prescribed to be only either positive, negative, or zero. The word "sign" is also often used to indicate binary aspects of mathematical or scientific objects, such as odd and even ( sign of a permutation), sense of orientation or rotation ( cw/ccw), one sided limits, and other concepts described in below. Sign of a number Numbers from various number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon]