Category:Absolute Value Function
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This category contains results about Absolute Value Function.
Definitions specific to this category can be found in Definitions/Absolute Value Function.
Let $x \in \R$ be a real number.
The absolute value of $x$ is denoted $\size x$, and is defined using the usual ordering on the real numbers as follows:
- $\size x = \begin{cases} x & : x > 0 \\ 0 & : x = 0 \\ -x & : x < 0 \end{cases}$
Subcategories
This category has the following 10 subcategories, out of 10 total.
A
- Absolute Difference (empty)
E
- Examples of Absolute Values (9 P)
F
N
- Negative of Absolute Value (4 P)
T
Pages in category "Absolute Value Function"
The following 45 pages are in this category, out of 45 total.
A
- Absolute Value Function is Completely Multiplicative
- Absolute Value Function is Continuous
- Absolute Value Function is Convex
- Absolute Value Function is Even Function
- Absolute Value Function on Integers induces Equivalence Relation
- Absolute Value induces Equivalence Compatible with Integer Multiplication
- Absolute Value induces Equivalence not Compatible with Integer Addition
- Absolute Value is Bounded Below by Zero
- Absolute Value is Many-to-One
- Absolute Value is Norm
- Absolute Value of Absolutely Continuous Function is Absolutely Continuous
- Absolute Value of Complex Cross Product is Commutative
- Absolute Value of Complex Dot Product is Commutative
- Absolute Value of Continuous Real Function is Continuous
- Absolute Value of Cut is Greater Than or Equal To Zero Cut
- Absolute Value of Cut is Zero iff Cut is Zero
- Absolute Value of Even Power
- Absolute Value of Negative
- Absolute Value of Power
- Absolute Value on Ordered Integral Domain is Strictly Positive except when Zero