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Abuse: Abuse is the improper usage or treatment of a thing, often to unfairly or improperly gain benefit. Abuse can come in many forms, such as: physical or verbal maltreatment, injury, assault, violation, rape, unjust practices, crimes, or other types of aggression.
Abuse of notation: In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help simplify the exposition or suggest the correct intuition . However, since the concept of formal/syntactical correctness depends on both time and context, many notations in mathematics that are flagged as abuse of notation in some context could be formally correct in other contexts.
Abuse of power: Abuse of power or abuse of authority, in the form of "malfeasance in office" or "official misconduct", is the commission of an unlawful act, done in an official capacity, which affects the performance of official duties. Malfeasance in office is often a just cause for removal of an elected official by statute or recall election.
Abuse of process: Abuse of process is a cause of action in tort arising from one party misusing or perverting regularly issued court process not justified by the underlying legal action. It is a common law intentional tort.