Numbers a and −a are opposites if they are the same distance from 0 but on different sides of the origin. The absolute value ∣a∣ is the distance from 0 to a; it is always non-negative.
Useful facts: ∣−a∣=∣a∣, ∣a∣=0 only when a=0.
Opposites: same distance from 0, opposite signs
∣a∣ — distance, never negative
∣−a∣=∣a∣
Opposite and absolute value
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