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VOOZH | about |
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VOOZH | about |
Let $x \in \R$ be a real number.
The of $x$ is denoted $\size x$, and is defined using the usual ordering on the real numbers as follows:
Let $x \in \R$ be a real number.
The of $x$ is denoted $\size x$, and is defined as:
where $+\sqrt {x^2}$ is the positive square root of $x^2$.
The graph of the can be presented as:
The applies to the various number classes as follows:
The notation $\cmod z$, where $z \in \C$, is defined as the modulus of $z$ and has a different meaning.
We can go still further back, and consider the general ordered integral domain:
Let $\struct {D, +, \times, \le}$ be an ordered integral domain whose zero is $0_D$.
Then for all $a \in D$, the absolute value of $a$ is defined as:
The of $x$ is sometimes called the modulus or magnitude of $x$, but note that modulus has a more specialized definition in the domain of complex numbers, and that magnitude has a more specialized definition in the context of vectors.
Some sources refer to it as the size of $x$.
Some sources call it the numerical value.
Some call it just the value, but that term is too broad to be reliable.
Let $x, a \in \R$.
Then:
$\mathsf{Pr} \infty \mathsf{fWiki}$ has a $\LaTeX$ shortcut for the symbol used to denote :
\size {x} .
If the argument of the \size command is $1$ character, then the braces {} are usually omitted.