The quality or state of being illogical or unreasonable. The irrationality of his decision was evident to everyone in the room.
A thought, action, or behavior that lacks reason or sound judgment. Her sudden outburst was an irrationality that surprised her colleagues.
The property of a real number of not being expressible as the ratio of two integers; the fact of being irrational in the mathematical sense. The irrationality of √2 was first proven by the ancient Greeks.