irrational

American Heritage® Dictionary of the English Language, Fourth Edition

1. adj. Not endowed with reason.
2. adj. Affected by loss of usual or normal mental clarity; incoherent, as from shock.
3. adj. Marked by a lack of accord with reason or sound judgment: an irrational dislike.
4. adj. Being a syllable in Greek and Latin prosody whose length does not fit the metric pattern.
5. adj. Being a metric foot containing such a syllable.
6. adj. Mathematics Of or relating to an irrational number.
7. n. Mathematics An irrational number.

Century Dictionary and Cyclopedia

1. Not rational; without the faculty of reason; void of understanding; unreasoning.
2. Without the quality of reason; contrary to reason; illogical; unreasonable: as, irrational motives; an irrational project.
3. In mathematics: In arithmetic, not capable of being exactly expressed by a vulgar fraction, proper or improper; surd. In mathematics irrational is a translation of Greek α%27λογον, inexpressible (by a fraction), opposed to ρ\ητόν. (See surd.) Every irrational quantity can, however, be conceived as expressed by an infinite continued fraction or interminate decimal.
4. 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.
5. 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.
6. In Greek prosody, incapable of measurement in terms of the fundamental or primary time or metrical unit.
7. n. That which is devoid of reason, as one of the lower animals.
8. n. A prime number.
9. n. 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.

Wiktionary

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

GNU Webster's 1913

1. adj. Not rational; void of reason or understanding.
2. adj. Not according to reason; having no rational basis; clearly contrary to reason; easily disproved by reasoning; absurd; -- of assertions and beliefs. foolish; unreasonable.
3. adj. (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.

WordNet 3.0

1. n. a real number that cannot be expressed as a rational number
2. adj. real but not expressible as the quotient of two integers
3. adj. not consistent with or using reason