Absolute Value Properties
If a, b and c are real numbers and their absolute values satisfy the following properties:
Properties of Absolute Value |
|
---|---|
Property | Statement |
Non-Negativity | Absolute of a number is always non-negative, | a | ≥ 0 |
Positive-Definiteness | |a| = 0 ↔ a = 0 |
Multiplicative Identity | |a × b| = |a| × |b| |
Subadditivity | |a + b| ≤ |a| + |b| |
Symmetry | |-a| = |a| |
Identity of Indiscernible | |a – b| = 0 ↔ a = b |
Triangle Inequality | |a – b| ≤ |a – c| + |c – b| |
Preservation of Division | |a / b| = |a| / |b| |
Equivalent to Subadditivity | |a ± b| ≥ | |a| – |b| | |
Absolute Value
Absolute Value for a number x is denoted by |x|, pronounced as “module x”. It is also referred to as numbers or magnitudes. Absolute values are only numeric values and do not include the sign of the numeric value.
Let’s learn about Absolute value in detail, including its symbol, properties, graph, and examples.
Table of Content
- What is Absolute Value?
- Absolute Values of a Number
- Absolute Value of 0
- Absolute Value Function
- Absolute Value Function Graphs
- Absolute Value of Complex Number
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