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Approximation
Related concepts and fundamentals:Agnosticism Epistemology Presupposition Probabilityv t eAn approximation is anything that is similar but not exactly equal to something else.Contents1 Etymology and usage 2 Mathematics 3 Science 4 Unicode 5 LaTeX Symbols 6 See also 7 References 8 External linksEtymology and usage[edit] The word approximation is derived from Latin
Latin
approximatus, from proximus meaning very near and the prefix ap- (ad- before p) meaning to.[1] Words like approximate, approximately and approximation are used especially in technical or scientific contexts
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Lenition
In linguistics, lenition is a kind of sound change that alters consonants, making them more sonorous. The word lenition itself means "softening" or "weakening" (from Latin
Latin
lenis = weak). Lenition can happen both synchronically (i.e. within a language at a particular point in time) and diachronically (i.e. as a language changes over time)
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Scientific Experiment
An experiment is a procedure carried out to support, refute, or validate a hypothesis. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale, but always rely on repeatable procedure and logical analysis of the results. There also exists natural experimental studies. A child may carry out basic experiments to understand gravity, while teams of scientists may take years of systematic investigation to advance their understanding of a phenomenon. Experiments and other types of hands-on activities are very important to student learning in the science classroom. Experiments can raise test scores and help a student become more engaged and interested in the material they are learning, especially when used over time.[1] Experiments can vary from personal and informal natural comparisons (e.g. tasting a range of chocolates to find a favorite), to highly controlled (e.g
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Function (mathematics)
In mathematics, a function[1] is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. Likewise, if the input is 3, then the output is also 9, and we may write f(3) = 9. (The same output may be produced by more than one input, but each input gives only one output.) The input variable(s) are sometimes referred to as the argument(s) of the function. Functions of various kinds are "the central objects of investigation"[2] in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input
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Shape
A shape is the form of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture or material composition. Psychologists have theorized that humans mentally break down images into simple geometric shapes called geons.[1] Examples of geons include cones and spheres.Contents1 Classification of simple shapes 2 Shape
Shape
in geometry2.1 Equivalence of shapes 2.2 Congruence and similarity 2.3 Homeomorphism3 Shape
Shape
analysis 4 Similarity classes 5 See also 6 References 7 External linksClassification of simple shapes[edit] Main article: Lists of shapesA variety of polygonal shapes.Some simple shapes can be put into broad categories. For instance, polygons are classified according to their number of edges as triangles, quadrilaterals, pentagons, etc. Each of these is divided into smaller categories; triangles can be equilateral, isosceles, obtuse, acute, scalene, etc
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Information
Information
Information
is any entity or form that resolves uncertainty or provides the answer to a question of some kind. It is thus related to data and knowledge, as data represents values attributed to parameters, and knowledge signifies understanding of real things or abstract concepts.[1] As it regards data, the information's existence is not necessarily coupled to an observer (it exists beyond an event horizon, for example), while in the case of knowledge, the information requires a cognitive observer.[citation needed] Information
Information
is conveyed either as the content of a message or through direct or indirect observation
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Functional Analysis
Functional analysis
Functional analysis
is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. The usage of the word functional as a noun goes back to the calculus of variations, implying a function whose argument is a function. The term was first used in Hadamard's 1910 book on that subject
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Real Number
In mathematics, a real number is a value that represents a quantity along a line. The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356..., the square root of 2, an irrational algebraic number). Included within the irrationals are the transcendental numbers, such as π (3.14159265...). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation, such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one
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Rational Number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.[1] Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Q (or blackboard bold Q displaystyle mathbb Q , Unicode ℚ);[2] it was thus denoted in 1895 by Giuseppe Peano
Giuseppe Peano
after quoziente, Italian for "quotient". The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for any other integer base (e.g
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Irrational Number
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself. Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the square root of two;[1][2][3] in fact all square roots of natural numbers, other than of perfect squares, are irrational. It can be shown that irrational numbers, when expressed in a positional numeral system (e.g
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History Of Science
The history of science is the study of the development of science and scientific knowledge, including both the natural and social sciences. (The history of the arts and humanities is termed history of scholarship.) Science
Science
is a body of empirical, theoretical, and practical knowledge about the natural world, produced by scientists who emphasize the observation, explanation, and prediction of real world phenomena. Historiography
Historiography
of science, in contrast, studies the methods employed by historians of science. The English word scientist is relatively recent—first coined by William Whewell
William Whewell
in the 19th century.[1] Previously, investigators of nature called themselves "natural philosophers"
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Latin
Latin
Latin
(Latin: lingua latīna, IPA: [ˈlɪŋɡʷa laˈtiːna]) is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet
Latin alphabet
is derived from the Etruscan and Greek alphabets, and ultimately from the Phoenician alphabet. Latin
Latin
was originally spoken in Latium, in the Italian Peninsula.[3] Through the power of the Roman Republic, it became the dominant language, initially in Italy and subsequently throughout the Roman Empire. Vulgar Latin
Vulgar Latin
developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Greek and French have contributed many words to the English language
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Correspondence Principle
In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers. In other words, it says that for large orbits and for large energies, quantum calculations must agree with classical calculations.[1] The principle was formulated by Niels Bohr
Niels Bohr
in 1920,[2] though he had previously made use of it as early as 1913 in developing his model of the atom.[3] The term codifies the idea that a new theory should reproduce under some conditions the results of older well-established theories in those domains where the old theories work. This concept is somewhat different from the requirement of a formal limit under which the new theory reduces to the older, thanks to the existence of a deformation parameter
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Physicists
A physicist is a scientist who has specialized knowledge in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. [1][2] Physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, to molecular length scales of chemical and biological interest, to cosmological length scales encompassing the Universe
Universe
as a whole
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Earth
Earth
Earth
is the third planet from the Sun
Sun
and the only object in the Universe
Universe
known to harbor life. According to radiometric dating and other sources of evidence, Earth
Earth
formed over 4.5 billion years ago.[24][25][26] Earth's gravity interacts with other objects in space, especially the Sun
Sun
and the Moon, Earth's only natural satellite. Earth
Earth
revolves around the Sun
Sun
in 365.26 days, a period known as an Earth
Earth
year
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball"[1]) is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to a circular object in two dimensions). Like a circle, which geometrically is an object in two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in three-dimensional space.[2] This distance r is the radius of the ball, and the given point is the center of the mathematical ball
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