 This diagram does not represent a "true" function, because the element 3 in X is associated with two elements, b and c, in Y. In mathematics, a multivalued function is a total relation; i.e. every input is associated with one or more outputs. Strictly speaking, a "well-defined" function associates one, and only one, output to any particular input. The term "multivalued function" is, technically, a misnomer: true functions are single-valued. However, a multivalued function from A to B can be represented as a function from A to the power set of B. -from the creater, wshun 02:20, 24 Dec 2004 (UTC) File links The following pages link to this file: Function (mathematics) Multivalued function Categories: FAL images ...
In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). ...
Mathematics, often abbreviated maths in Commonwealth English and math in American English, is the study of abstraction. ...
In mathematics, the concept of binary relation is exemplified by such ideas as is greater than and is equal to in arithmetic, or is congruent to in geometry, or is an element of or is a subset of in set theory. ...
Information processsing In information processing, input is the process of receiving information from an object. ...
Information processing In information processing, output is the process of transmitting information (verb usage). ...
In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). ...
Information processing In information processing, output is the process of transmitting information (verb usage). ...
Information processsing In information processing, input is the process of receiving information from an object. ...
In mathematics, given a set S, the power set of S, written P(S) or 2S, is the set of all subsets of S. In formal language, the existence of power set of any set is presupposed by the axiom of power set. ...
Examples - Inverse trigonometric functions are multiple-valued because trigonometric functions are periodic. We have
- Consequently arctan(1) may be thought of as having multiple values: π/4, 5π/4, −3π/4, and so on.
- The natural logarithm function from the positive reals to the reals is single-valued, but its generalization to complex numbers (excluding 0) is multiple-valued, because the natural exponential function exp(z) (evaluated at complex arguments z) is periodic with period 2πi. Denoting this multi-valued function by "Log", with a capital "L" to distinguish it from its single-valued counterpart defined only for positive real arguments, the values assumed by Log(e) are 1 + 2πin for all integers n.
Multivalued functions of a complex variable have branch points. For the nth root and logarithm functions, 0 is a branch point; for the arctangent functions, the imaginary units i and −i are branch points. The text or formatting below is generated by a template which has been proposed for deletion. ...
The complex numbers are an extension of the real numbers, in which all non-constant polynomials have roots. ...
In mathematics, the principal square root of a non-negative real number is denoted and represents the non-negative real number whose square (the result of multiplying the number by itself) is . ...
The natural logarithm is the logarithm to the base e, where e is approximately equal to 2. ...
The integers consist of the positive natural numbers (1, 2, 3, …) the negative natural numbers (−1, −2, −3, ...) and the number zero. ...
In complex analysis, a branch point may be thought of informally as a point z0 at which a multiple_valued function changes values when one winds once around z0. ...
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