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The domain of a function is the set of inputs accepted by the function. It can be defined by a formula, a graph, or a restriction of a larger set. Learn more about different types of domains and examples.
Learn the difference between codomain and image of a function, and how to use the term "range" correctly. See examples, definitions, and references for more details.
Learn the definitions and properties of image and preimage of functions and binary relations in mathematics. Image is the output value or the set of output values of a function, while preimage is the input value or the set of input values that produce a given output value.
In complex analysis, a complex domain (or simply domain) is any connected open subset of the complex plane C. For example, the entire complex plane is a domain, as is the open unit disk, the open upper half-plane, and so forth. Often, a complex domain serves as the domain of definition for a holomorphic function.
A function is a mathematical concept that assigns to each element of a set exactly one element of another set. Learn the history, definition, types, properties, and examples of functions in mathematics.
An interval is a set of real numbers lying between two endpoints with no gaps. Learn about different types of intervals, such as open, closed, half-open, and degenerate, and how to denote them with various notations.
Codomain is the set of possible outputs of a function, while range is the set of actual outputs. Learn how codomain affects function properties, such as surjectivity and composition, and see examples of codomain and range in different contexts.
A continuous function is a function that has no abrupt changes in value, or equivalently, whose graph is a single unbroken curve. Learn the definition, history, and examples of continuous functions in terms of limits, neighborhoods, and topology.
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