irrational

The word “irrational” means not based on logic or reason; unfounded or nonsensical. In plain terms, not making logical sense — or, in math, a number that goes on forever without repeating and can't be written as a simple fraction.

“Irrational” is pronounced ih-RASH-nuhl (/ɪˈɹæʃ.(ə.)nəl/ in IPA).

Here is “irrational” used in a sentence: “He had an irrational fear of elevators.”

“Irrational” is an adjective.

The word “irrational” comes from Latin. From Latin irratiōnālis, from ir- ("not") plus ratiōnālis ("rational").

“Irrational” is an uncommon word in modern English, usually learned at around the B2 level.

“Irrational” has 2 distinct senses listed in this dictionary. The most common is: not based on logic or reason; unfounded or nonsensical.

Irrational describes something not based on logic or reason, often emphasizing emotion or fear over sense, such as an irrational fear. Illogical focuses more narrowly on a flaw in reasoning or argument structure, such as a conclusion that doesn't follow from its premises. Irrational is broader and often carries an emotional undertone that illogical lacks.

An irrational number is a real number that cannot be written as a fraction of two whole numbers, meaning its decimal representation never ends or repeats. Well-known examples include numbers like pi and the square root of two.

Rational numbers can be expressed as a fraction of two whole numbers, such as 1/2 or 3, while irrational numbers cannot be written this way and have non-terminating, non-repeating decimal expansions. Every real number is either rational or irrational, but not both.