In mathematics, the logarithm is the inverse operation to exponentiation, just as division is the inverse of multiplication. That means the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number. In the most simple case the logarithm counts repeated multiplication of the same factor; e.g., since 1000 = 10 × 10 × 10 = 103, the "logarithm to base 10" of 1000 is 3. More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm can be calculated for any two positive real numbers b and x where b is not equal to 1. The logarithm of x to base b, denoted logb (x) (or logb x when no confusion is possible), is the unique real number y such that by = x. For example, log2 64 = 6, as 64 = 26. The logarithm to base 10 (that is b = 10) is called the common logarithm and has many applications in science and engineering
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity,[1] structure,[2] space,[1] and change.[3][4][5] It has no generally accepted definition.[6][7] Mathematicians seek out patterns[8][9] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist
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Psychophysics
Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics
Psychophysics has been described as "the scientific study of the relation between stimulus and sensation"[1] or, more completely, as "the analysis of perceptual processes by studying the effect on a subject's experience or behaviour of systematically varying the properties of a stimulus along one or more physical dimensions".[2] Psychophysics
Psychophysics also refers to a general class of methods that can be applied to study a perceptual system. Modern applications rely heavily on threshold measurement,[3] ideal observer analysis, and signal detection theory.[4] Psychophysics
Psychophysics has widespread and important practical applications
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An aqueous solution is a solution in which the solvent is water. It is usually shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be represented as Na+(aq) + Cl−(aq). The word aqueous means pertaining to, related to, similar to, or dissolved in, water. As water is an excellent solvent and is also naturally abundant, it is a ubiquitous solvent in chemistry. Substances that are hydrophobic ('water-fearing') often do not dissolve well in water, whereas those that are hydrophilic ('water-friendly') do. An example of a hydrophilic substance is sodium chloride. Acids and bases are aqueous solutions, as part of their Arrhenius definitions. The ability of a substance to dissolve in water is determined by whether the substance can match or exceed the strong attractive forces that water molecules generate between themselves
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In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula
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Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage
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Frequency
Frequency is the number of occurrences of a repeating event per unit of time.[1] It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency.[2] For example, if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second (that is, 60 seconds divided by 120 beats)
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In mathematics, Stirling's approximation
Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of n
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In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5 ! = 5 × 4 × 3 × 2 × 1 = 120. displaystyle 5!=5times 4times 3times 2times 1=120. The value of 0! is 1, according to the convention for an empty product.[1] The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic occurrence is the fact that there are n! ways to arrange n distinct objects into a sequence (i.e., permutations of the set of objects)
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Forensic accounting, forensic accountancy or financial forensics is the specialty practice area of accounting that describes engagements that result from actual or anticipated disputes or litigation. "Forensic" means "suitable for use in a court of law", and it is to that standard and potential outcome that forensic accountants generally have to work. Forensic accountants, also referred to as forensic auditors or investigative auditors, often have to give expert evidence at the eventual trial.[1] All of the larger accounting firms, as well as many medium-sized and boutique firms and various police and government agencies have specialist forensic accounting departments. Within these groups, there may be further sub-specializations: some forensic accountants may, for example, just specialize in insurance claims, personal injury claims, fraud, anti-money-laundering, construction,[2] or royalty audits.[3] Financial forensic engagements may fall into several categories
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A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.[1] Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre". Measurement
Measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to the present
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A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1, which is called an imaginary number because there is no real number that satisfies this equation. For the complex number a + bi, a is called the real part, and b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.[1][2] The complex number system can be defined as the algebraic extension of the ordinary real numbers by an imaginary number i.[3] This means that complex numbers can be added, subtracted, and multiplied, as polynomials in the variable i, with the rule i2 = −1 imposed. Furthermore, complex numbers can also be divided by nonzero complex numbers
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Public key cryptography, or asymmetrical cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner. This accomplishes two functions: authentication, where the public key verifies that a holder of the paired private key sent the message, and encryption, where only the paired private key holder can decrypt the message encrypted with the public key. In a public key encryption system, any person can encrypt a message using the receiver's public key. That encrypted message can only be decrypted with the receiver's private key. To be practical, the generation of a public and private key -pair must be computationally economical. The strength of a public key cryptography system relies on the computational effort (work factor in cryptography) required to find the private key from its paired public key
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In arithmetic and algebra, the cube of a number n is its third power: the result of the number multiplied by itself twice:n3 = n × n × n.It is also the number multiplied by its square:n3 = n × n2.This is also the volume formula for a geometric cube with sides of length n, giving rise to the name. The inverse operation of finding a number whose cube is n is called extracting the cube root of n. It determines the side of the cube of a given volume. It is also n raised to the one-third power. Both cube and cube root are odd functions:(−n)3 = −(n3).The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3. The graph of the cube function f: x → x3 (or the equation y = x3) is known as the cubic parabola
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.svg/440px-Three_apples(1).svg.png "Go To List2 -> Natural Number")
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country")
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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
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