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Elementary special functions

Summary Of: Absolute value

3 is the absolute value of both 3 and... The absolute value of a number... Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings... For example an absolute value is also defined for the... The absolute value is closely related to the notions of... The graph of the absolute value function for real numbers... The graph of the absolute value function for real numbers... The graph of the absolute value function for real numbers... the absolute value of a real number is the... and more generally the absolute value of the difference of two real numbers is the distance between them... be seen to be a generalization of the absolute value of the difference... The absolute value has the following four fundamental properties... The absolute value of a complex number z is the distance r from z to the origin... The absolute value of a complex number z is the distance r from z to the origin... The absolute value of a complex number... the definition given above for the real absolute value cannot be directly generalized for a complex number... It follows that the absolute value of a real number... is equal to its absolute value considered as a complex number since... Similar to the geometric interpretation of the absolute value for real numbers... that the absolute value of a complex number is the distance in the... that the absolute value of the difference of two complex numbers is equal to the distance between those two... The complex absolute value shares all the properties of the real absolute value given in Propositions 2 and 3... absolute value function is continuous everywhere but... The definition of absolute value given for real numbers above can easily be extended to any... The absolute value is closely related to the idea of distance... the absolute value of a real or complex number is the... the absolute value of the difference of two real or complex numbers is the distance between them... The properties of the absolute value of the difference of two real or complex numbers... of the real absolute value function is the... The absolute value function is not differentiable at... Where the absolute value function of a real number returns a value without respect to its sign... The absolute value function has no concavity at any point... The absolute value function is also integrable... The fundamental properties of the absolute value for real numbers given in Proposition 2 above... can be used to generalize the notion of absolute value to an arbitrary field... An absolute value which satisfies any... Again the fundamental properties of the absolute value for real numbers can be used... The complex absolute value is a special case of the norm in an... functions compute the absolute value of an operand... giving the absolute value of the negative value in...

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value (philosophy) | mathematics | real number | sign | computer programming | function | complex numbers | quaternions | ordered rings | fields | vector spaces | magnitude | distance | norm | The graph of the absolute value function for real numbers. | | Jean-Robert Argand | Karl Weierstrass | real number | positive | zero | negative | distance | real number line | distance function | identity | Multiplicativeness | Subadditivity | Symmetry | Identity of indiscernibles | Triangle inequality | The absolute value of a complex number z is the distance r from z to the origin. It is also seen in the picture that z and its complex conjugate z have the same absolute value. | | complex conjugate | complex numbers | ordered | Pythagorean theorem | complex plane | origin | complex conjugate | endomorphism | multiplicative group | continuous | differentiable | monotonically decreasing | even function | invertible | complex | Cauchy-Riemann equations | idempotent | nonlinear | ordered ring | additive inverse | identity element | distance | Euclidean distance | Euclidean n-space | distance function | derivative | sign function | Heaviside step function | real number line | antiderivative | field | absolute value | identity element | ultrametric | bounded | Archimedean | Norm (mathematics) | vector space | Euclidean space | Euclidean norm | R1 | norm | p-norm | inner product space | complex plane | Euclidean plane | C programming language | floating-point | infinities | not-a-number | Fortran | Matlab | GNU Octave | assembly language | register | x86 architecture | Intel | two's complement | Oxford English Dictionary | Littré | Lazare Nicolas M. Carnot | Oxford English Dictionary | ISBN 0898714206 | ISBN 0-534-37718-1 | PlanetMath | Eric W. Weisstein | MathWorld | ISBN 0-691-02795-1 | ISBN 0-12-622760-8 | Absolute value (algebra) | Valuation (mathematics) | Categories | Elementary special functions |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Absolute value".