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Division By Zero
In mathematics, division by zero, division (mathematics), division where the divisor (denominator) is 0, zero, is a unique and problematic special case. Using fraction notation, the general example can be written as \tfrac a0, where a is the dividend (numerator). The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplication, multiplied by the divisor. That is, c = \tfrac ab is equivalent to c \cdot b = a. By this definition, the quotient q = \tfrac is nonsensical, as the product q \cdot 0 is always 0 rather than some other number a. Following the ordinary rules of elementary algebra while allowing division by zero can create a mathematical fallacy, a subtle mistake leading to absurd results. To prevent this, the arithmetic of real numbers and more general numerical structures called field (mathematics), fields leaves division by zero undefined (mathematics), undefined, and situations where division by zero might occur m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal Function
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yields the original number (since the product of the number and its reciprocal is 1). The term ''reciproca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Singularity
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the reciprocal function f(x) = 1/x has a singularity at x = 0, where the value of the function is not defined, as involving a division by zero. The absolute value function g(x) = , x, also has a singularity at x = 0, since it is not differentiable there. The algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane cu ... defined by \left\ in the (x, y) coordinate system has a singularity (called a cusp (singularity), cusp) at (0, 0). For singularities in algebraic geometry, see singular point of an algebraic variety. For singul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slopes As Ratios
In mathematics, the slope or gradient of a line is a number that describes the direction of the line on a plane. Often denoted by the letter ''m'', slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same number for any choice of points. The line may be physical – as set by a road surveyor, pictorial as in a diagram of a road or roof, or abstract. An application of the mathematical concept is found in the grade or gradient in geography and civil engineering. The ''steepness'', incline, or grade of a line is the absolute value of its slope: greater absolute value indicates a steeper line. The line trend is defined as follows: *An "increasing" or "ascending" line goes from left to right and has positive slope: m>0. *A "decreasing" or "descending" line goes from left to right and has negative slope: m<0. Special directions are: *A "(square) |
Mechanical Calculator
A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or a simulation like an analog computer or a slide rule. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator and the digital computer. Surviving notes from Wilhelm Schickard in 1623 reveal that he designed and had built the earliest known apparatus fulfilling the widely accepted definition of a mechanical calculator (a counting machine with an automated tens-carry). His machine was composed of two sets of technologies: first an abacus made of Napier's bones, to simplify multiplications and divisions first described six years earlier in 1617, and for the mechanical part, it had a dialed pedometer to perform additions and subtractions. A study of the surviving notes shows a machine that could have jammed after a few entries on the same dial. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite Loop
In computer programming, an infinite loop (or endless loop) is a sequence of instructions that, as written, will continue endlessly, unless an external intervention occurs, such as turning off power via a switch or pulling a plug. It may be intentional. There is no general algorithm to determine whether a computer program contains an infinite loop or not; this is the halting problem. Overview This differs from "a type of computer program that runs the same instructions continuously until it is either stopped or interrupted". Consider the following pseudocode: how_many = 0 while is_there_more_data() do how_many = how_many + 1 end display "the number of items counted = " how_many ''The same instructions'' were run ''continuously until it was stopped or interrupted'' . . . by the ''FALSE'' returned at some point by the function ''is_there_more_data''. By contrast, the following loop will not end by itself: birds = 1 fish = 2 while birds + fish > 1 do birds = 3 - bird ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subtraction
Subtraction (which is signified by the minus sign, –) is one of the four Arithmetic#Arithmetic operations, arithmetic operations along with addition, multiplication and Division (mathematics), division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches. Therefore, the ''difference'' of 5 and 2 is 3; that is, . While primarily associated with natural numbers in arithmetic, subtraction can also represent removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, Fraction (mathematics), fractions, irrational numbers, Euclidean vector, vectors, decimals, functions, and matrices. In a sense, subtraction is the inverse of addition. That is, if and only if . In words: the difference of two numbers is the number that gives the first one when added to the second one. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lettuce Sandwich
A lettuce sandwich is a wrap with lettuce substituted for the bread, or a sandwich with a filling consisting primarily of lettuce. It should not be confused with other sandwiches that use lettuce as one of many ingredients, such as the BLT sandwich or the tomato and lettuce sandwich. The lettuce sandwich has a long history in both the United States and the United Kingdom. It has been used as a metaphor to represent things like mundanity, weakness and poverty. In more recent times, the lettuce sandwich, including lettuce hamburgers have symbolized diets including the keto diet. History The lettuce sandwich was mentioned in print as early as 1894 in ''The Century Illustrated Monthly Magazine''. The lettuce sandwich (bread with a lettuce filling) was a common food in the United States and England during the first half of the 20th century. The “Veggie Delight” sandwich from Subway restaurants is an example of a fast food version of the Lettuce Sandwich. Lettuce sandwiches have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crash (computing)
In computing, a crash, or system crash, occurs when a computer program such as a software application or an operating system stops functioning properly and exits. On some operating systems or individual applications, a crash reporting service will report the crash and any details relating to it (or give the user the option to do so), usually to the developer(s) of the application. If the program is a critical part of the operating system, the entire system may crash or hang, often resulting in a kernel panic or fatal system error. Most crashes are the result of a software bug. Typical causes include accessing invalid memory addresses, incorrect address values in the program counter, buffer overflow, overwriting a portion of the affected program code due to an earlier bug, executing invalid machine instructions (an illegal or unauthorized opcode), or triggering an unhandled exception. The original software bug that started this chain of events is typically considere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Real Number Line
In mathematics, the extended real number system is obtained from the real number system \R by adding two elements denoted +\infty and -\infty that are respectively greater and lower than every real number. This allows for treating the potential infinities of infinitely increasing sequences and infinitely decreasing series as actual infinities. For example, the infinite sequence (1,2,\ldots) of the natural numbers increases ''infinitively'' and has no upper bound in the real number system (a potential infinity); in the extended real number line, the sequence has +\infty as its least upper bound and as its limit (an actual infinity). In calculus and mathematical analysis, the use of +\infty and -\infty as actual limits extends significantly the possible computations. It is the Dedekind–MacNeille completion of the real numbers. The extended real number system is denoted \overline, \infty,+\infty/math>, or \R\cup\left\. When the meaning is clear from context, the symbol +\inf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer
A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as Computer program, ''programs'', which enable computers to perform a wide range of tasks. The term computer system may refer to a nominally complete computer that includes the Computer hardware, hardware, operating system, software, and peripheral equipment needed and used for full operation; or to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of Programmable logic controller, industrial and Consumer electronics, consumer products use computers as control systems, including simple special-purpose devices like microwave ovens and remote controls, and factory devices like industrial robots. Computers are at the core of general-purpose devices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity Symbol
The infinity symbol () is a mathematical symbol representing the concept of infinity. This symbol is also called a ''lemniscate'', after the lemniscate curves of a similar shape studied in algebraic geometry, or "lazy eight", in the terminology of livestock branding. This symbol was first used mathematically by John Wallis in the 17th century, although it has a longer history of other uses. In mathematics, it often refers to infinite processes ( potential infinity) rather than infinite values ( actual infinity). It has other related technical meanings, such as the use of long-lasting paper in bookbinding, and has been used for its symbolic value of the infinite in modern mysticism and literature. It is a common element of graphic design, for instance in corporate logos as well as in older designs such as the Métis flag. The infinity symbol and several variations of the symbol are available in various character encodings. History The lemniscate has been a common decorativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
