# 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 8 subcategories, out of 8 total.

## 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