irrational

/i'ræʃənl/

Thân thiện

An irrational fear of spiders can be very distressing.

Definition

1. Adjective:

   • Not based on or using clear, logical thought; not reasonable: Describes feelings, fears, or behavior that are not governed by reason or logic.
   • (Mathematics) Of a number: real but not expressible as a quotient of two integers: Describes a number that cannot be written as a simple fraction.

2. Noun:

   • (Mathematics) A real number that cannot be expressed as a rational number: A number like π or √2.

Usage Examples

• Adjective:

  • His fear of clowns is completely irrational. (This feeling is not based on logical reasoning.)
  • Pi is an irrational number. (This number cannot be expressed as a fraction.)

• Noun:

  • The square root of two is a well-known irrational. (This is a specific type of real number.)

Advanced Usage

• "Irrational exuberance": Excessive, unfounded optimism in financial markets, not justified by economic fundamentals.

  • The economist warned of irrational exuberance in the stock market.

• "Irrational belief": A conviction held despite a lack of evidence or contrary evidence.

  • The cult was based on a series of irrational beliefs.

Variants and Related Words

• Irrationality (n): The quality or state of being irrational.

  • The irrationality of his decision shocked everyone.

• Irrationalize (v): (Rare) To make irrational.

• Irrationalism (n): A philosophical system or attitude emphasizing the non-rational.

Synonyms

• Adjective (illogical sense): Unreasonable, illogical, unfounded, absurd.
• Adjective (mathematical sense): Surd (specifically for roots).

Antonyms

• Adjective: Rational, reasonable, logical, sensible.
• Noun: Rational number.

Học thuật

Adjective

1. real but not expressible as the quotient of two integers
   • irrational numbers
2. not consistent with or using reason
   • irrational fears
   • irrational animals

Noun

1. a real number that cannot be expressed as a rational number

Từ đồng nghĩa

• irrational number