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List of mathematical symbols

List of mathematical symbols
When reading the list, it is important to recognize that a mathematical concept is independent of the symbol chosen to represent it. For many of the symbols below, the symbol is usually synonymous with the corresponding concept (ultimately an arbitrary choice made as a result of the cumulative history of mathematics), but in some situations a different convention may be used. For example, depending on context, the triple bar "≡" may represent congruence or a definition. Further, in mathematical logic, numerical equality is sometimes represented by "≡" instead of "=", with the latter representing equality of well-formed formulas. In short, convention dictates the meaning. Each symbol is shown both in HTML, whose display depends on the browser's access to an appropriate font installed on the particular device, and in TeX, as an image. Guide[edit] This list is organized by symbol type and is intended to facilitate finding an unfamiliar symbol by its visual appearance. Basic symbols[edit]

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Mandelbrot Set The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of points in the complex plane such that the corresponding Julia set is connected and not computable. "The" Mandelbrot set is the set obtained from the quadratic recurrence equation with Approximation An approximation is anything that is similar but not exactly equal to something else. The term can be applied to various properties (e.g. value, quantity, image, description) that are nearly but not exactly correct; similar, but not exactly the same e.g. The approximate time was 10 o'clock.

Introduction to Embodiments of Mind by Warren S. McCulloch Introduction to Embodiments of Mind by Warren S. McCulloch By Seymour Papert Power law An example power-law graph, being used to demonstrate ranking of popularity. To the right is the long tail, and to the left are the few that dominate (also known as the 80–20 rule). In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another.

Sample space For example, if the experiment is tossing a coin, the sample space is typically the set {head, tail}. For tossing two coins, the corresponding sample space would be {(head,head), (head,tail), (tail,head), (tail,tail)}. For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).[2] Outline of combinatorics The following outline is presented as an overview of and topical guide to combinatorics: Combinatorics – branch of mathematics concerning the study of finite or countable discrete structures. Essence of combinatorics[edit] Main article: Combinatorics Branches of combinatorics[edit] How investigating mediators and moderators helps explain intervention effects How mediators and moderators help explain intervention effects 3Moderators are variables that are present among the population prior to an intervention. Since they arepresent prior to randomization in the case of a trial, moderators should be equally distributed across allgroups. As a result they should not be statistically correlated with treatment status.

Mind–body problem Different approaches toward resolving the mind–body problem. The mind–body problem in philosophy examines the relationship between mind and matter, and in particular the relationship between consciousness and the brain. Each of these categories itself contains numerous variants. The two main forms of dualism are substance dualism, which holds that the mind is formed of a distinct type of substance not governed by the laws of physics, and property dualism, which holds that mental properties involving conscious experience are fundamental properties, alongside the fundamental properties identified by a completed physics. The three main forms of monism are physicalism, which holds that the mind consists of matter organized in a particular way; idealism, which holds that only thought truly exists and matter is merely an illusion; and neutral monism, which holds that both mind and matter are aspects of a distinct essence that is itself identical to neither of them. Philosophers David L.

THE LAST DAYS OF THE POLYMATH People who know a lot about a lot have long been an exclusive club, but now they are an endangered species. Edward Carr tracks some down ... From INTELLIGENT LIFE Magazine, Autumn 2009 Sigma-algebra If X = {a, b, c, d}, one possible σ-algebra on X is Σ = {∅, {a, b}, {c, d}, {a, b, c, d}}, where ∅ is the empty set. However, a finite algebra is always a σ-algebra. If {A1, A2, A3, …} is a countable partition of X then the collection of all unions of sets in the partition (including the empty set) is a σ-algebra.

Calculating the Distance to the Horizon For Any Game Home Up Site Map Assumptions | Method 1 | Method 2 Method 1 | Method 2 This is all based on the assumption that the horizon is the point on the world's surface at which the line of sight of the viewer, whatever their height, becomes parallel (tangential) to the surface of the world, and meets the surface of the world (so that the viewer cannot see any further than it). It also assumes a perfectly spherical world, and does not take into account any effects on the visible horizon due to terrain or atmospheric refraction.

9.5.1 What is heterogeneity? Home > Part 2: General methods for Cochrane reviews > 9 Analysing data and undertaking meta-analyses > 9.5 Heterogeneity > 9.5.1 What is heterogeneity? 9.5.1 What is heterogeneity? Inevitably, studies brought together in a systematic review will differ. Any kind of variability among studies in a systematic review may be termed heterogeneity. It can be helpful to distinguish between different types of heterogeneity. Variability in the participants, interventions and outcomes studied may be described as clinical diversity (sometimes called clinical heterogeneity), and variability in study design and risk of bias may be described as methodological diversity (sometimes called methodological heterogeneity).

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