In mathematics, the absolute value of an integer is defined as its distance from zero on the number line, regardless of direction. This means that each positive integer has a corresponding negative integer that shares the same absolute value. For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5. Therefore, for any integer x, it is true that:
- If x is a positive integer (e.g., 7), then both 7 and -7 have the absolute value of 7.
- If x is zero (0), then the absolute value is simply 0 since there is no counterpart.
- If x is a negative integer (e.g., -3), then the absolute values are identical to that of its positive counterpart (e.g., 3).
Thus, we can conclude that for any non-zero integer, there are exactly two different integers that have the same absolute value. These are the integer itself and its negative counterpart. For 0, there is only one integer which is 0 itself that has the absolute value of 0.