irrational

Meanings

1. 1
   adj

   not consistent with or using reason

   irrational fears

2. 2
   adj

   real but not expressible as the quotient of two integers

   irrational numbers

3. 3
   adj

   Not rational; unfounded, nonsensical or wrong-headed.

   an irrational decision

4. 4
   adj

   Of a real number, that cannot be written as the ratio of two integers.

   The number π is irrational.

5. 5
   noun

   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.

6. 6
   noun

   a real number that cannot be expressed as a rational number

Etymology

From Latin irratiōnālis, from ir- + ratiōnālis.