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  2. Restriction (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Restriction_(mathematics)

    More generally, the restriction (or domain restriction or left-restriction) of a binary relation between and may be defined as a relation having domain , codomain and graph ( ) = {(,) ():}. Similarly, one can define a right-restriction or range restriction R B . {\displaystyle R\triangleright B.}

  3. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    The principal value of the multifunction is chosen at a particular point and values elsewhere in the domain of definition are defined to agree with those found by analytic continuation. For example, for the square root, the principal value is defined as the square root that has a positive real part. This defines a single valued analytic ...

  4. Domain of a function - Wikipedia

    en.wikipedia.org/wiki/Domain_of_a_function

    In layman's terms, the domain of a function can generally be thought of as "what x can be". [1] More precisely, given a function :, the domain of f is X. In modern mathematical language, the domain is part of the definition of a function rather than a property of it.

  5. Function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Function_(mathematics)

    The domain of definition of such a function is the set of inputs for which the algorithm does not run forever. A fundamental theorem of computability theory is that there cannot exist an algorithm that takes an arbitrary general recursive function as input and tests whether 0 belongs to its domain of definition (see Halting problem).

  6. Surjective function - Wikipedia

    en.wikipedia.org/wiki/Surjective_function

    Interpretation for surjective functions in the Cartesian plane, defined by the mapping f : X → Y, where y = f(x), X = domain of function, Y = range of function. Every element in the range is mapped onto from an element in the domain, by the rule f. There may be a number of domain elements which map to the same range element.

  7. Domain theory - Wikipedia

    en.wikipedia.org/wiki/Domain_theory

    Domain theory is a branch of mathematics that studies special kinds of ... an even stronger restriction on a partially ordered set is given by requiring the existence ...

  8. Domain (ring theory) - Wikipedia

    en.wikipedia.org/wiki/Domain_(ring_theory)

    In algebra, a domain is a nonzero ring in which ab = 0 implies a = 0 or b = 0. [1] (Sometimes such a ring is said to "have the zero-product property".) Equivalently, a domain is a ring in which 0 is the only left zero divisor (or equivalently, the only right zero divisor). A commutative domain is called an integral domain.

  9. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_trigonometric...

    Domain of cotangent and cosecant : The domains of and are the same. They are the set of all angles θ {\displaystyle \theta } at which sin ⁡ θ ≠ 0 , {\displaystyle \sin \theta \neq 0,} i.e. all real numbers that are not of the form π n {\displaystyle \pi n} for some integer n , {\displaystyle n,}