irrational
/ɪˈræʃənl/ (bre, ipa) · /ɪˈræʃənl/ (ame, ipa) · /i-ˈra-sh(ə-)nəl ˌi(r)-/ (ame, mw)
irrational — adjective
- irrationalpositive
- more irrationalcomparative
- most irrationalsuperlative
1. used to describe thoughts, feelings, or actions that are based on strong emotion
used to describe thoughts, feelings, or actions that are based on strong emotions such as fear or anger rather than on clear reasoning or facts.
Theo's fear of spiders is completely irrational, since none in his country are dangerous.
collocation: completely irrational
The committee made an irrational decision when they refused to look at the new evidence.
collocation: irrational decision
Ingrid knew her worry was irrational, but she checked the door three times before bed.
It is irrational to spend your whole salary on lottery tickets instead of rent.
Raj's irrational anger during the meeting surprised everyone who knew him as a calm person.
- unreasonable
broader; can describe a person, demand, or situation that is not fair or sensible
- illogical
focuses on flaws in reasoning rather than emotion-driven behaviour
- absurd
more extreme; describes something so unreasonable it is ridiculous
- groundless
specifically about fears or beliefs that have no basis in fact
- rational
based on clear reason and good judgment
- logical
following the rules of correct reasoning
- reasonable
fair, sensible, and based on facts
文法句型
it is irrational to + infinitive
an irrational + noun
irrational that + clause
用法筆記
Frequently describes emotions or behaviours that the person themselves may recognise as unreasonable (e.g., irrational fear, irrational jealousy). Subject can be a person, an emotion, or a decision.
常見錯誤
2. describes a number you cannot write exactly in the form a/b where a and b are wh
describes a number you cannot write exactly in the form a/b where a and b are whole numbers — for example, the square root of 2 or pi.
The square root of two is itself irrational — its digits never form a repeating pattern.
example: square root of two as irrational number
Students learn about irrational numbers when they study geometry in high school.
Pi is a famous irrational — you cannot write it as a simple fraction.
The teacher explained that irrational numbers have decimal parts that go on forever.
Mathematicians discovered irrational numbers more than two thousand years ago.
- non-terminating
describes a decimal that continues without end, a property shared by some irrational numbers
- non-repeating
describes a decimal with no repeating pattern, a defining feature of irrational numbers
- rational
can be expressed as a fraction of two whole numbers
文法句型
irrational + number/noun
用法筆記
Used only in mathematical contexts to classify numbers such as √2, √3, and π. In everyday language, the 'NOT LOGICAL' sense (sense 1) is the one people encounter far more often.
常見錯誤
irrational — noun
1. any real number that you cannot write as a fraction made from two integers; for
any real number that you cannot write as a fraction made from two integers; for instance, the square root of 2 or pi.
An irrational cannot be written as a fraction like three-quarters.
countable noun: an irrational
The teacher asked the class to name three irrationals they had studied.
plural form: irrationals
Every point on the number line is either a rational or an irrational.
Decimals of irrationals never end and never fall into a repeating pattern.
The ancient Greeks were surprised to find that some lengths are irrationals.
- irrational number
the full, more formal term; preferred in academic writing
文法句型
an irrational
the irrational
用法筆記
A technical mathematics term. In academic writing the full phrase 'irrational number' is more common; the standalone noun 'irrational' (countable) appears mainly in classroom or textbook contexts where the meaning is already clear.