To write the absolute value of an integer, you enclose the integer within two vertical lines. According to the reference, the absolute value of an integer is its distance from zero, regardless of its sign. This is represented by two vertical lines |a|, also known as the modulus of a.
Understanding Absolute Value
The absolute value is a concept in mathematics that deals with the magnitude of a number, irrespective of its sign (positive or negative).
- It's the distance of a number from zero on the number line.
- Absolute values are always non-negative (either positive or zero).
Representation and Examples
The absolute value of an integer (or any real number) 'a' is written as |a|.
Here are some examples to illustrate this:
- |5| = 5 (The absolute value of 5 is 5)
- |-5| = 5 (The absolute value of -5 is also 5)
- |0| = 0 (The absolute value of 0 is 0)
As indicated in the reference, 5 is the absolute value for both 5 and -5.
Practical Applications
Absolute values are used in various mathematical and real-world scenarios, including:
- Distance Calculation: Determining the distance between two points.
- Error Analysis: Calculating the magnitude of error without considering its direction.
- Computer Programming: In algorithms where only the magnitude of a number is relevant.
Summary
| Integer | Absolute Value |
|---|---|
| 5 | |
| -5 | |
| 0 | |
| -10 | |
| 100 |
