Reading Theme:
Irrational Definition, Examples, and Usage Guide (2 meaning)
Meaning 1：illogical (irrational)
irrational
/ɪˈræʃənəl/
adj.
Doing things based on feelings, not logical thinking.
illogical
➕
/ɪˈlɒdʒɪkəl/
adj.
Acting or thinking based on emotions or instincts rather than reason or evidence.
📘 Details & Usage
📖 Root Explanation
From Latin in- (not) + rationalis (reason), referring to lack of reason or logic.
💡 Mnemonic
Imagine a 'rat' that runs in circles without logic: 'I-rational' -> 'I am a rat, no reason'.
📖 Example
She knew spiders in her country were harmless, but her irrational fear made her scream every time she saw one.
She knew spiders in her country were harmless, but her irrational fear made her scream every time she saw one.
🔗 Collocations
irrational behavior – Actions not based on reason
irrational fear – Unreasonable or excessive fear
irrational decision – A choice made without logical thought
🔄 Synonyms
unreasonable (adj.) – Not guided by reason or good judgment
absurd (adj.) – Wildly unreasonable or illogical
illogical (adj.) – Contrary to the rules of logic
🚫 Antonyms
rational (adj.) – Based on or in accordance with reason
logical (adj.) – Characterized by clear, sound reasoning
reasonable (adj.) – Fair and sensible
🌱 Derivatives
irrationally (adv.) – In a way that is not based on reason
irrationality (n.) – The state or quality of being irrational
📖 Cultural Story
The term 'irrational' in mathematics was first used by medieval scholars to translate Greek 'alogos' (without ratio). It later expanded to describe unreasonable behavior in psychology and everyday speech.
Meaning 2：non-repeating decimal (irrational)
irrational
/ɪˈræʃənəl/
adj.
A number that cannot be written as a simple fraction.
non-repeating decimal
➕
/nɒn rɪˈpiːtɪŋ ˈdesɪməl/
adj.
A number that cannot be expressed as a ratio of two integers and has an infinite, non-repeating decimal expansion.
📘 Details & Usage
📖 Example
In math class, the teacher explained that numbers like π and √2 are irrational because their decimal places go on forever without repeating.
In math class, the teacher explained that numbers like π and √2 are irrational because their decimal places go on forever without repeating.
🔗 Collocations
irrational number – A number not expressible as a fraction
prove irrational – Demonstrate that a number is not rational
irrational value – An exact numeric quantity that is irrational
🔄 Synonyms
non-rational (adj.) – Not rational; used especially for numbers
incommensurable (adj.) – Not having a common factor or measure
surd (n.) – An irrational root, especially a square root
🚫 Antonyms
rational (adj.) – Able to be expressed as a ratio of integers
integer (n.) – A whole number (a type of rational number)
terminating decimal (n.) – A decimal that ends after a finite number of digits
🌱 Derivatives
irrationality (n.) – The property of being irrational (in mathematics)
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