irrational
UK: ɪˈræʃənəl | US: ɪˈræʃənəl
adj. not based on or using reason or logic
adj. (mathematics) (of a number) not expressible as a ratio of integers
The word "irrational" originates from Latin irrationalis, combining the negative prefix ir- (variant of in- before "r") with rationalis (from ratio, meaning "reason" or "calculation"). The root ratio evolved into English "reason" and "rational," while ir- negates the meaning. The term initially described illogical thought but later expanded to mathematics for numbers like √2 that cannot be expressed as fractions.
His fear of spiders was completely irrational.
The decision seemed irrational to everyone involved.
√2 is an example of an irrational number.
She regretted her irrational outburst during the meeting.
Ancient Greeks discovered the existence of irrational numbers.