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34 relations: Analytic function, Banach algebra, Basis (linear algebra), Bijection, Binomial theorem, Characterization (mathematics), Closure (mathematics), Conformal map, Continuous function, Derivative, E (mathematical constant), Edwin Hewitt, Exponential function, Factorial, Fundamental theorem of calculus, Harmonic series (mathematics), Initial value problem, Integral, Integral test for convergence, Lebesgue integration, Limit (mathematics), Limit of a function, Limit superior and limit inferior, Mathematics, Measurable function, Monotonic function, Natural logarithm, Proof that e is irrational, Ratio test, Sequence, Series (mathematics), Taylor series, Walter Rudin, Well-defined.
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Banach algebra
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, i.e. a normed space and complete in the metric induced by the norm.
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Basis (linear algebra)
In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Binomial theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
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Characterization (mathematics)
In mathematics, the statement that "Property P characterizes object X" means that not only does X have property P, but that X is the only thing that has property P. In other words, P is a defining property of X. It is also common to find statements such as "Property Q characterises Y up to isomorphism".
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Closure (mathematics)
A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.
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Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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E (mathematical constant)
The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.
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Edwin Hewitt
Edwin Hewitt (January 20, 1920, Everett, Washington – June 21, 1999) was an American mathematician known for his work in abstract harmonic analysis and for his discovery, in collaboration with Leonard Jimmie Savage, of the Hewitt–Savage zero–one law.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
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Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.
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Harmonic series (mathematics)
In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are,,, etc., of the string's fundamental wavelength.
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Initial value problem
In mathematics, the field of differential equations, an initial value problem (also called the Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Integral test for convergence
In mathematics, the integral test for convergence is a method used to test infinite series of non-negative terms for convergence.
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Lebesgue integration
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis.
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Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value.
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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.
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Limit superior and limit inferior
In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (i.e., eventual and extreme) bounds on the sequence.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Measurable function
In mathematics and in particular measure theory, a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable, analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open.
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Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
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Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
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Proof that e is irrational
The number ''e'' was introduced by Jacob Bernoulli in 1683.
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Ratio test
In mathematics, the ratio test is a test (or "criterion") for the convergence of a series where each term is a real or complex number and is nonzero when is large.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Walter Rudin
Walter Rudin (May 2, 1921 – May 20, 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison.
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Well-defined
In mathematics, an expression is called well-defined or unambiguous if its definition assigns it a unique interpretation or value.
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Redirects here:
Definitions of e, Definitions of the exponential function, Proof of e as a limit.
References
[1] https://en.wikipedia.org/wiki/Characterizations_of_the_exponential_function
