without the faculty of reason; deprived of reason.

without or deprived of normal mental clarity or sound judgment.

not in accordance with reason; utterly illogical

irrational arguments.

not endowed with the faculty of reason

irrational animals.

Mathematics .

(of a number) not capable of being expressed exactly as a ratio of two integers.

(of a function) not capable of being expressed exactly as a ratio of two polynomials.

Algebra . (of an equation) having an unknown under a radical sign or, alternately, with a fractional exponent.

Greek and Latin Prosody .

of or pertaining to a substitution in the normal metrical pattern, esp. a long syllable for a short one.

noting a foot or meter containing such a substitution.

Mathematics . irrational number.

adjective

logical , rational , reasonable , reflective , sensible , sound , stable

adjective

aberrant , absurd , brainless , cockamamie , crazy , delirious , demented , disconnected , disjointed , distraught , fallacious , flaky * , foolish , freaky , incoherent , injudicious , insane , invalid , kooky , loony * , mad , mindless , nonsensical , nutty * , off-the-wall , preposterous , raving , reasonless , ridiculous , silly , sophistic , specious , stupid , unreasonable , unreasoning , unsound , unstable , unthinking , unwise , wacky * , wild , wrong , illogical , unreasoned , addlepated , alogical , asinine , fanatical , fatuous , grotesque , imbecilic , pathological , psychotic , senseless , surreal , transcendental , unbounded , unfounded