In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0 and 1, as well as all numbers between them. Other examples of intervals are the set of all real numbers, the set of all negative real numbers, and the empty set.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q, which stands 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.
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Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of operations that combine numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers.
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Horner's method
In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S. ) is either of two things: (i) an algorithm for calculating polynomials, which consists in transforming the monomial form into a computationally efficient form; or (ii) a method for approximating the roots of a polynomial. The latter is also known as Ruffini–Horner's method. These methods are named after the British mathematician William George Horner, although they were known before him.
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Monotonic function
In mathematics, a monotonic function (or monotone function) is a function that preserves the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.
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Approximation
An approximation is a representation of something that is not exact, but still close enough to be useful. Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. Approximations may be used because incomplete information prevents use of exact representations. Many problems in physics are either too complex to solve analytically, or impossible to solve using the available analytical tools.
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Open set
In topology, a set is called an open set if it is a neighborhood of every point . When dealing with metric spaces, this can be intuitively interpreted as saying that every can be "moved" some non-zero distance, in any direction, and it will still lie within . The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined.
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