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Definition of irrational : 1. Not according to reason; absurd; foolish.
2. Not capable of being exactly expressed by an integral number, or by a vulgar fraction; surd; - said especially of roots. See Surd.
3. Not rational; void of reason or understanding; as, brutes are irrational animals.

Synonyms:

irrational number, inconsequent, ill-judged, unreasoning, inconclusive, unsound, ill-advised, unreasonable, blind, jaundiced, wrong, yellow, mistaken, reason, monstrous, weak, false, erroneous, inconsequential, reasonless, superstitious, incorrect, incoherent, out of bounds, wild, unreasoned, childish, extreme, irresponsible, illegitimate, specious, perverse, nonrational, untenable, chimerical, ill-considered, infatuated, anomalous

idiotic, nonsensical, incongruous, absurd, farcical, invalid, crazy, impossible, foolish, inconsistent, paradoxical, implausible, ridiculous, outlandish, bizarre, ludicrous, illogical, meaningless, anachronistic, silly, senseless, preposterous, stupid, inane, eccentric, contradictory, fallacious, self-contradictory

demented, psycho, berserk, frenzied, feverish, neurotic, delirious, blithering, maniacal, babbling, lunatic, hysterical, kooky, batty, unbalanced, psychotic, mad, schizoid, insane, crack-brained, brain-sick, nutty, deranged

Usage examples:

• Oh, my friend, say what you please, argue how you like, this crowding together of men and women in unnatural surroundings, this haste to be rich in material things, this attempt to enjoy without production, this removal from first- hand life, is irrational, and the end of it is ruin. - "Adventures In Contentment", David Grayson AKA: Ray Stannard Baker.
• There were now negative numbers, irrational numbers such as square roots, and imaginary numbers such as square roots of negative numbers. - "Our Legal Heritage, 4th Ed.", S. A. Reilly.
• But, if even irrational love, etc. - "The Ego and His Own", Max Stirner.