Exponentiation and Function composition

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Difference between Exponentiation and Function composition

Exponentiation vs. Function composition

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent. In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

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Algebraic structure

In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.

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Associative property

In mathematics, the associative property is a property of some binary operations.

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Cartesian product

In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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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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Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

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Fractal

In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Functional square root

In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition.

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Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

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Infinite set

In set theory, an infinite set is a set that is not a finite set.

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Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.

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Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

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Iterated function

In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times.

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

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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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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Monoid

In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

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Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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TeX

TeX (see below), stylized within the system as TeX, is a typesetting system (or "formatting system") designed and mostly written by Donald Knuth and released in 1978.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

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Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

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