irrational

This word describes a disconnect between evidence and action. It often carries a critical or clinical tone, suggesting that a person is being governed by panic, obsession, or instinct rather than a calculated thought process. While "unreasonable" might imply a stubborn refusal to compromise, "irrational" implies a failure of the cognitive process itself. In a mathematical context, the word loses its emotional baggage and becomes a precise technical classification. Here, it describes a specific structural property of a number, shifting from a judgment of character or logic to a description of infinite, non-repeating numerical sequences.