Irrationality
WordNet
noun
(1) The state of being irrational; lacking powers of understanding
WiktionaryText
Etymology
From ancient Greece
circa 500 B.C.
"Irrational" originally meant only that a number could not be expressed as a ratio. But for the pythagoreans it came to mean something threatening, a hint that their world view might not make sense, which is today the other meaning of "irrational".
- ir- + rational
Adjective
- Not rational; unfounded or nonsensical.
- an irrational decision
- (no comparative or superlative) Of a real number, that cannot be written as the ratio of two integers.
- The number π is irrational.
Noun
- A real number that can not be expressed as the quotient of two integers, an irrational number.
- the quotient of two irrationals a and b is a rational if and only if there is an integer n>0 and an integer m such that a*n = b*m