Additive opposites MUST have the same absolute values.
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The absolute value is always non-negative. So, the absolute values of zero and positive integers are the same as the numbers. However, the absolute values of negative integers are their additive inverses or additive opposites (or positive equivalents).Thus, for example, abs(-3) = +3
Yes.
Different.
X and Y have the same absolute value because the opposite of a number doesn't change its distance from zero. The absolute value of a number represents its distance from zero on the number line, and since X and Y are opposites, they have the same distance from zero.
A positive and negative number with the same magnitude (value) will have their absolute values equal.