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A curve (with endpoints) is a continuous function whose domain is the unit interval [0, 1]. In the most general form, the range of such a function may lie in an arbitrary topological space , but in the most commonly studied cases, the range will lie in a Euclidean space such as the 2-dimensional plane (a planar curve ) or the 3-dimensional ...
A closed interval is an interval that includes all its endpoints and is denoted with square brackets. [2] For example, [0, 1] means greater than or equal to 0 and less than or equal to 1 . Closed intervals have one of the following forms in which a and b are real numbers such that a ≤ b : {\displaystyle a\leq b\colon }
The use of intervals for the range or domain of a function is very common. A solution which makes the reason for the different brackets around an interval more plain is to use one of the templates {{open-closed}}, {{closed-open}}, {}, {{closed-closed}}. For instance: {{open-closed | −π, π}} produces (−π, π].
In addition to its role in real analysis, the unit interval is used to study homotopy theory in the field of topology. In the literature, the term "unit interval" is sometimes applied to the other shapes that an interval from 0 to 1 could take: (0,1], [0,1), and (0,1). However, the notation I is most commonly reserved for the closed interval [0,1].
The term domain is also commonly used in a different sense in mathematical analysis: a domain is a non-empty connected open set in a topological space. In particular, in real and complex analysis , a domain is a non-empty connected open subset of the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} or the complex coordinate space C n ...
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.
This template determines which interval a given value lies in. The intervals are defined by the unnamed parameters. The value to be determined is named parameter n. format=time can also be passed to the template. If set, the intervals and value will be compared as times (and if n is not provided, it will evaluate as the current timestamp).
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.