Loosely, equality is the state of being quantitatively the same. More formally, equality (or the identity relation) is the binary relation on a set X defined by . The identity relation is the archetype of the more general concept of an equivalence relation on a set: those binary relations which are reflexive, symmetric, and transitive. The relation of equality is also antisymmetric.
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Sequence
In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements), and the number of ordered element (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function. For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters.
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Limit of a function
Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1. In other words, the limit of (sin x)/x as x approaches zero equals 1.
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Bracket
Brackets are tall punctuation marks used in matched pairs within text, to set apart or interject other text. Used unqualified, brackets refer to different types of brackets in different parts of the world and in different contexts.
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Finite set
In mathematics, a finite set is a set that has a finite number of elements. For example, is a finite set with five elements. The number of elements of a finite set is a natural number, and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite: Finite sets are particularly important in combinatorics, the mathematical study of counting.
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Function (mathematics)
In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is –3, then the output is 9, and we may write f(–3) = 9.
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Big O notation
In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation, or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g. , in their processing time or working space requirements) to changes in input size.
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Random number generation
A random number generator (RNG) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random. The many applications of randomness have led to the development of several different methods for generating random data. Many of these have existed since ancient times, including dice, coin flipping, the shuffling of playing cards, the use of yarrow stalks (by divination) in the I Ching, and many other techniques.
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