irrational

Etymology

From Latin irratiōnālis, from ir- + ratiōnālis.

adj

1. Not rational; unfounded or nonsensical.
   an irrational decision
   July 18, 2012, Scott Tobias, AV Club The Dark Knight Riseshttp://www.avclub.com/articles/the-dark-knight-rises-review-batman,82624/ Where the Joker preys on our fears of random, irrational acts of terror, Bane has an all-consuming, dictatorial agenda that’s more stable and permanent, a New World Order that’s been planned out with the precision of a military coup.
2. (mathematics, arithmetic, number theory, not comparable) Of a real number, that cannot be written as the ratio of two integers.
   The number π is irrational.

noun

1. A real number that can not be expressed as the quotient of two integers, an irrational number.
   The square root of 2, which was the first irrational to be discovered, was known to the early Pythagoreans, and ingenious methods of approximating to its value were discovered. 1946, Bertrand Russell, History of Western Philosophy, I.24