irrational

from The American Heritage® Dictionary of the English Language, 5th Edition.

• adjective Not endowed with reason.
• adjective Affected by loss of usual or normal mental clarity; incoherent, as from shock.
• adjective Marked by a lack of accord with reason or sound judgment.
• adjective Being a syllable in Greek and Latin prosody whose length does not fit the metric pattern.
• adjective Being a metric foot containing such a syllable.
• adjective Mathematics Of or relating to an irrational number.
• noun An irrational number.

from The Century Dictionary.

• Not rational; without the faculty of reason; void of understanding; unreasoning.
• Without the quality of reason; contrary to reason; illogical; unreasonable: as, irrational motives; an irrational project.
• In mathematics: In arithmetic, not capable of being exactly expressed by a vulgar fraction, proper or improper; surd.
• In translations of Euclid, and cognate writings, at once incommensurable with the assumed unit and not having its square commensurable with that of the unit. This is the peculiar meaning given by Euclid to α%27λογος, though Plato uses it in sense , above.
• In algebra, noting a quantity involving a variable raised to a fractional power; or. in a wider sense, noting a quantity not rational, not a sum of products of constants and of variables into one another or into themselves.
• In Greek prosody, incapable of measurement in terms of the fundamental or primary time or metrical unit.
• noun That which is devoid of reason, as one of the lower animals.
• noun A prime number.
• noun In mathematics, an irrational number, that is, the mark of a cut which separates all rational numbers into two classes, the first having no greatest number, the second no least.

from the GNU version of the Collaborative International Dictionary of English.

• adjective Not rational; void of reason or understanding.
• adjective Not according to reason; having no rational basis; clearly contrary to reason; easily disproved by reasoning; absurd; -- of assertions and beliefs.
• adjective (Math.) Not capable of being exactly expressed by an integral number, nor by a ratio of integral numbers; surd; -- said especially of roots. See Surd.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• adjective Not rational; unfounded or nonsensical.
• adjective mathematics, arithmetic, number theory, not comparable Of a real number, that cannot be written as the ratio of two integers.
• noun A real number that can not be expressed as the quotient of two integers, an irrational number.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a real number that cannot be expressed as a rational number
• adjective real but not expressible as the quotient of two integers
• adjective not consistent with or using reason