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An approximation (represented by the symbol ≈) is an inexact representation of something that is still close enough to be useful. A related article is titled Uncertainty. For statistical certainty see Probability. Nihilism (from the Latin nihil, nothing is a philosophical position that argues that Existence is without objective meaning Purpose Agnosticism ( Greek: α- a-, without + γνώσις gnōsis, knowledge after Gnosticism) is the philosophical view that the Uncertainty is a term used in subtly different ways in a number of fields including Philosophy, Statistics, Economics, Finance, Insurance Probability is the likelihood or chance that something is the case or will happen Belief is the psychological state in which an individual holds a Proposition or Premise to be true Epistemology (from Greek επιστήμη - episteme, "knowledge" + λόγος, " Logos " or theory of knowledge A related article is titled Uncertainty. For statistical certainty see Probability. Determinism is the philosophical Proposition that every event including human cognition and behaviour decision and action is causally determined Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. A number is an Abstract object, tokens of which are Symbols used in Counting and measuring. The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function The shape ( OE sceap Eng created thing) of an object located in some space refers to the part of space occupied by the object as determined A physical law or scientific law is a Scientific generalization based on empirical Observations of physical behavior (i
Approximations may be used because incomplete information prevents use of exact representations. Information as a concept has a diversity of meanings from everyday usage to technical settings Many problems in physics are either too complex to solve analytically, or impossible to solve. Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly.
For instance, physicists often approximate the shape of the Earth as a sphere even though more accurate representations are possible, because many physical behaviours—e. Below is a list of famous Physicists Many of these from the 20th and 21st centuries are found on the list of recipients of the Nobel Prize in physics. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe g. gravity—are much easier to calculate for a sphere than for less regular shapes. Gravitation is a natural Phenomenon by which objects with Mass attract one another
The problem consisting of two or more planets orbiting around a sun has no exact solution. Often, ignoring the gravitational effects of the planets gravitational pull on each other and assuming that the sun does not move achieve a good approximation. The use of perturbations to correct for the errors can yield more accurate solutions. Simulations of the motions of the planets and the star also yields more accurate solutions.
The type of approximation used depends on the available information, the degree of accuracy required, the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation. Information as a concept has a diversity of meanings from everyday usage to technical settings
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Science
The scientific method is carried out with a constant interaction between scientific laws (theory) and empirical measurements, which are constantly compared to one another. Scientific method refers to bodies of Techniques for investigating phenomena Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as
The approximation also refers to using a simpler process. This model is used to make predictions easier. The most common versions of philosophy of science accept that empirical measurements are always approximations—they do not perfectly represent what is being measured. Philosophy of science is the study of assumptions foundations and implications of Science. Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as The history of science indicates that the scientific laws commonly felt to be true at any time in history are only approximations to some deeper set of laws. Science is a body of empirical, theoretical, and practical knowledge about the natural world, produced by a global community of researchers For example, attempting to resolve a model using outdated physical laws alone incorporates an inherent source of error, which should be corrected by approximating the quantum effects not present in these laws. Note The term model has a different meaning in Model theory, a branch of Mathematical logic. Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects
Each time a newer set of laws is proposed, it is required that in the limiting situations in which the older set of laws were tested against experiments, the newer laws are nearly identical to the older laws, to within the measurement uncertainties of the older measurements. In Mathematics, the concept of a " limit " is used to describe the Behavior of a function as its argument either "gets close" In scientific inquiry an experiment ( Latin: Ex- periri, "to try out" is a method of investigating particular types of research questions or Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as This is the correspondence principle. This article discusses quantum theory For other uses see Correspondence principle (disambiguation.
Mathematics
Approximation usually occurs when an exact form or an exact numerical number is unknown. However some known form may exist and may be able to represent the real form so that no significant deviation can be found. Numerical approximations sometimes result from using a small number of significant digits. In Mathematics and Computer science, a digit is a symbol (a number symbol e Approximation theory is a branch of mathematics, a quantitative part of functional analysis. In Mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with Quantitatively For functional analysis as used in psychology see the Functional analysis (psychology article Diophantine approximation deals with approximation to real numbers by rational numbers. In Number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of Real numbers by Rational In Mathematics, the real numbers may be described informally in several different ways In Mathematics, a rational number is a number which can be expressed as a Ratio of two Integers Non-integer rational numbers (commonly called fractions The symbol "≈" means "approximately equal to"; tilde (~) and the Libra sign (
) are common alternatives. Libra is the seventh Astrological sign in the Zodiac, originating from the constellation of Libra.
See also
References
In the mathematical field of Numerical analysis, the approximation error in some data is the discrepancy between an exact value and some approximation to it Estimation is the calculated Approximation of a result which is usable even if Input data may be incomplete or uncertain. In Physics, particularly in physics Education, a Fermi problem, Fermi question, or Fermi estimate is an Estimation problem designed In Mathematics, a linear approximation is an approximation of a general function using a Linear function (more precisely an Affine function In Numerical analysis, Newton's method (also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson) is perhaps the Numerical analysis is the study of Algorithms for the problems of continuous mathematics (as distinguished from Discrete mathematics) Orders of approximation have been used not only in Science, Engineering, and other quantitative disciplines to make Approximations with various degrees In Numerical analysis, the Runge–Kutta methods (pronounced /ˌʀuŋgeˈkuta/ are an important family of implicit and explicit iterative methods for the approximation of solutions A successive approximation ADC is a type of Analog-to-digital converter that converts a continuous analog waveform into a discrete Digital representation In Mathematics, the Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its Derivatives The method of least squares is used to solve Overdetermined systems Least squares is often applied in statistical contexts particularly Regression analysis.Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic