The absolute value of an integer a represents its distance from zero on the number line, irrespective of its sign.
Understanding Absolute Value
The absolute value, also known as the modulus, of an integer a is denoted by |a|. According to the reference, the absolute value of any integer, whether positive or negative, results in a non-negative real number. This real number represents the magnitude, or size, of the original integer.
Examples of Absolute Value
| Integer (a) | Absolute Value (|a|) | Explanation |
| :------------ | :------------------- | :-------------------------------------------------------------------------- |
| 5 | 5 | The distance of 5 from 0 is 5. |
| -5 | 5 | The distance of -5 from 0 is 5. |
| 0 | 0 | The distance of 0 from 0 is 0. |
| -10 | 10 | The distance of -10 from 0 is 10. |
Representing Absolute Value
The absolute value of a can be defined as follows:
- |a| = a, if a ≥ 0
- |a| = -a, if a < 0
In simpler terms:
- If a is a positive integer or zero, then the absolute value of a is simply a.
- If a is a negative integer, then the absolute value of a is the negation of a (which makes it positive).
Practical Implications
Understanding absolute value is important in various mathematical and real-world applications. For instance, when dealing with distances, errors, or magnitudes where only the size matters, the concept of absolute value is used.
