Search results
Results From The WOW.Com Content Network
The preceding kinds of definitions, which had prevailed since Aristotle's time, [4] were abandoned in the 19th century as new branches of mathematics were developed, which bore no obvious relation to measurement or the physical world, such as group theory, projective geometry, [3] and non-Euclidean geometry.
In mathematics, for a function :, the image of an input value is the single output value produced by when passed . The preimage of an output value y {\displaystyle y} is the set of input values that produce y {\displaystyle y} .
A concept definition is similar to the usual notion of a definition in mathematics, with the distinction that it is personal to an individual: "a personal concept definition can differ from a formal concept definition, the latter being a concept definition which is accepted by the mathematical community at large." [1]
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
Examples include e and π. Trigonometric number: Any number that is the sine or cosine of a rational multiple of π. Quadratic surd: A root of a quadratic equation with rational coefficients. Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number.
In a category with all finite limits and colimits, the image is defined as the equalizer (,) of the so-called cokernel pair (,,), which is the cocartesian of a morphism with itself over its domain, which will result in a pair of morphisms ,:, on which the equalizer is taken, i.e. the first of the following diagrams is cocartesian, and the second equalizing.
In constructive mathematics, an apartness relation is a constructive form of inequality, and is often taken to be more basic than equality. An apartness relation is often written as # {\displaystyle \#} (⧣ in unicode ) to distinguish from the negation of equality (the denial inequality ), which is weaker.
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]