(idiom) to make trouble without reason; to be deliberately provocative or stir up trouble willfully

arbitrary; acting in a way that is both rude and lacking in any reason

A real number that cannot be expressed as a simple fraction of two integers and has a non-repeating, infinite decimal expansion

an algebraic expression that contains at least one variable within a radical or raised to a fractional power

without truth or reason on one's side, one cannot go even a single inch; paired antonym of [[有理走遍天下|有理走遍天下|you3 li3 zou3 bian4 tian1 xia4]]

lacking reason, logic, or rationality; the state or quality of being irrational