Search results
Results from the WOW.Com Content Network
The real absolute value function is an example of a continuous function that achieves a global minimum where the derivative does not exist. The subdifferential of | x | at x = 0 is the interval [−1, 1]. [14] The complex absolute value function is continuous everywhere but complex differentiable nowhere because it violates the Cauchy–Riemann ...
The standard absolute value on the integers. The standard absolute value on the complex numbers.; The p-adic absolute value on the rational numbers.; If R is the field of rational functions over a field F and () is a fixed irreducible polynomial over F, then the following defines an absolute value on R: for () in R define | | to be , where () = () and ((), ()) = = ((), ()).
For example, the absolute value of −3 and the absolute value of 3 are both equal to 3. This is written in symbols as | −3 | = 3 and | 3 | = 3. In general, any arbitrary real value can be specified by its magnitude and its sign. Using the standard encoding, any real value is given by the product of the magnitude and the sign in standard ...
For example, saying "the absolute value is denoted by | · |" is perhaps clearer than saying that it is denoted as | |. ± (plus–minus sign) 1. Denotes either a plus sign or a minus sign. 2. Denotes the range of values that a measured quantity may have; for example, 10 ± 2 denotes an unknown value that lies between 8 and 12.
The vertical bar is used as a mathematical symbol in numerous ways. If used as a pair of brackets, it suggests the notion of the word "size". These are: absolute value: | |, read "the absolute value of x" [2] cardinality: | |, read "the cardinality of the set S" or "the length of a string S"
For example, the absolute value function is identical to in the region >, whose derivative is the constant value +1, which equals the value of there. Because the absolute value is a convex function , there is at least one subderivative at every point, including at the origin.
Obtaining the absolute value of a number is a unary operation. ... Symbol Description Example Increment ++ Increases the value of a variable by 1: x = 2; ++x; // x is ...
In some fonts (for example Arial) they are only symmetrical in certain sizes. Alternatively the quotes can be rendered as ⌈ and ⌉ (U+2308 and U+2309) or by using a negation symbol and a reversed negation symbol ⌐ ¬ in superscript mode.)