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In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively. [1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval. [2]
Typically data is discretized into partitions of K equal lengths/width (equal intervals) or K% of the total data (equal frequencies). [1] Mechanisms for discretizing continuous data include Fayyad & Irani's MDL method, [2] which uses mutual information to recursively define the best bins, CAIM, CACC, Ameva, and many others [3]
Data (/ ˈ d eɪ t ə / DAY-tə, US also / ˈ d æ t ə / DAT-ə) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of ...
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]
Hilbert matrix — example of a matrix which is extremely ill-conditioned (and thus difficult to handle) Wilkinson matrix — example of a symmetric tridiagonal matrix with pairs of nearly, but not exactly, equal eigenvalues; Convergent matrix — square matrix whose successive powers approach the zero matrix; Algorithms for matrix multiplication:
The three most popular examples of calculus on time scales are differential calculus, difference calculus, and quantum calculus. Dynamic equations on a time scale have a potential for applications such as in population dynamics. For example, they can model insect populations that evolve continuously while in season, die out in winter while ...
Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.
Digital data can be contrasted with analog data, which is represented by a value from a continuous range of real numbers. Analog data is transmitted by an analog signal, which not only takes on continuous values but can vary continuously with time, a continuous real-valued function of time. An example is the air pressure variation in a sound wave.