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Polychotomous Key
Polychotomous key refers to the number of alternatives which a decision point may have in a non-temporal hierarchy of independent variables. The number of alternatives are equivalent to the root or nth root of a mathematical or logical variable. Decision points or independent variables with two states have a binary root that is referred to as a dichotomous key whereas, the term polychotomous key refers to roots which are greater than one or unitary and usually greater than two or binary. Polychotomous keys are used in troubleshooting to build troubleshooting charts and in classification/identification schemes with characteristics that have more than one attribute and the order of characteristics is not inherently based on the progression of time. See also *Number prefix *Polychotomy A polychotomy (päl′i kät′ə mē; plural ''polychotomies'') is a division or separation into many parts or classes. Polychotomy is a generalization of dichotomy, which is a polychotomy of exact ...
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Nth Root
In mathematics, a radicand, also known as an nth root, of a number ''x'' is a number ''r'' which, when raised to the power ''n'', yields ''x'': :r^n = x, where ''n'' is a positive integer, sometimes called the ''degree'' of the root. A root of degree 2 is called a ''square root'' and a root of degree 3, a ''cube root''. Roots of higher degree are referred by using ordinal numbers, as in ''fourth root'', ''twentieth root'', etc. The computation of an th root is a root extraction. For example, 3 is a square root of 9, since 3 = 9, and −3 is also a square root of 9, since (−3) = 9. Any non-zero number considered as a complex number has different complex th roots, including the real ones (at most two). The th root of 0 is zero for all positive integers , since . In particular, if is even and is a positive real number, one of its th roots is real and positive, one is negative, and the others (when ) are non-real complex numbers; if is even and is a negative real numbe ...
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Dichotomy
A dichotomy is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are complements. In logic, the partitions are opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multi categorical variables as binary variables is called dichotomization. The discretization error inherent in dichotomization is temporarily ignored for modeling purposes. Etymology The term '' ...
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Troubleshooting
Troubleshooting is a form of problem solving, often applied to repair failed products or processes on a machine or a system. It is a logical, systematic search for the source of a problem in order to solve it, and make the product or process operational again. Troubleshooting is needed to identify the symptoms. Determining the most likely cause is a process of elimination—eliminating potential causes of a problem. Finally, troubleshooting requires confirmation that the solution restores the product or process to its working state. In general, troubleshooting is the identification or diagnosis of "trouble" in the management flow of a system caused by a failure of some kind. The problem is initially described as symptoms of malfunction, and troubleshooting is the process of determining and remedying the causes of these symptoms. A system can be described in terms of its expected, desired or intended behavior (usually, for artificial systems, its purpose). Events or inputs t ...
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Number Prefix
Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: * unicycle, bicycle, tricycle (1-cycle, 2-cycle, 3-cycle) * dyad, triad (2 parts, 3 parts) * biped, quadruped (2 legs, 4 legs) * September, October, November, December (month 7, month 8, month 9, month 10) * decimal, hexadecimal (base-10, base-16) * septuagenarian, octogenarian (70-79 years old, 80-89 years old) * centipede, millipede (around 100 legs, around 1000 legs) In many European languages there are two principal systems, taken from Latin and Greek, each with several subsystems; in addition, Sanskrit occupies a marginal position. There is also an international set of metric prefixes, which are used in the metric system and which for the most part are either distorted from the forms below or not based on actual number words. Table of number prefixes in English In the following pr ...
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Polychotomy
A polychotomy (päl′i kät′ə mē; plural ''polychotomies'') is a division or separation into many parts or classes. Polychotomy is a generalization of dichotomy, which is a polychotomy of exactly two parts. In evolutionary biology, the term polychotomy can also be considered a historically-based misspelling of polytomy.Weiss, David J. (1995). “Polychtomous or Polytomous?,” Applied Psychological Measurement, Vol. 19, No. 1, p. 4 See also * Polychotomous key Polychotomous key refers to the number of alternatives which a decision point may have in a non-temporal hierarchy of independent variables. The number of alternatives are equivalent to the root or nth root of a mathematical or logical variable. D ... References {{Reflist External links Examples of usageAnother Approach to Polychotomous Classification
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Concepts In Logic
Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by several disciplines, such as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach called cognitive science. In contemporary philosophy, there are at least three prevailing ways to understand what a concept is: * Concepts as mental representations, where concepts are entities that exist in the mind (mental objects) * Concepts as abilities, where concepts are abilities peculiar to cognitive agents (mental states) * Concepts as Fregean senses, where concepts are abstract objects, as opposed to mental obje ...
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Decision Theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome. There are three branches of decision theory: # Normative decision theory: Concerned with the identification of optimal decisions, where optimality is often determined by considering an ideal decision-maker who is able to calculate with perfect accuracy and is in some sense fully rational. # Prescriptive decision theory: Concerned with describing observed behaviors through the use of conceptual models, under the assumption that those making the decisions are behaving under some consistent rules. # Descriptive decision theory: Analyzes how individuals actually make the decisions that they do. Decision theory is closely related to the field of game theory and is an interdisciplinary topic, studied by econom ...
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