irreducible

/,iri'dju:səbl/

Thân thiện

An irreducible fraction cannot be simplified any further.

Definition

1. Adjective:
   • Incapable of being made smaller, simpler, or less complex: Describes something that cannot be reduced to a more basic or fundamental form, state, or amount.
   • Incapable of being changed back to a normal or original condition: Used in specific contexts, such as medicine, to describe a condition that cannot be reversed or restored.

Usage and Examples

• General Use (Incapable of being reduced):

  • The scientist argued that these were irreducible elements of the theory. (They are fundamental components that cannot be simplified further.)
  • After cutting all unnecessary expenses, we have reached an irreducible minimum budget. (This is the smallest possible budget; it cannot be made any smaller.)

• Mathematics (Incapable of simplification):

  • The fraction 3/7 is an irreducible fraction because 3 and 7 share no common factors. (It cannot be simplified to a fraction with smaller integers.)
  • The polynomial was proven to be irreducible over the field of rational numbers. (It cannot be factored into polynomials of lower degree with rational coefficients.)

• Medical Use (Incapable of being restored):

  • The patient was diagnosed with an irreducible hernia, requiring immediate surgery. (The hernia could not be pushed back or returned to its normal position non-surgically.)

Advanced Usage

• "Irreducible complexity": A concept, often used in debates about evolution, describing a system that is argued to cease functioning if any one of its parts is removed, implying it could not have evolved by successive small modifications.

  • The argument of irreducible complexity is frequently cited by proponents of intelligent design.

• Philosophical/Scientific Use: Describing a fundamental, non-derivable principle or entity.

  • Consciousness is considered by some philosophers to be an irreducible aspect of reality.

Variants and Related Words

• Irreducibly (adverb): In an irreducible manner.
  • The two concepts are irreducibly linked.
• Irreducibility (noun): The quality or state of being irreducible.
  • The irreducibility of the equation was central to the proof.

Synonyms

• Indivisible: Incapable of being divided or separated.
• Elemental: Of or being a fundamental, basic part.
• Unsimplifiable: Not able to be made simpler. (Less common)
• Inalterable: Not able to be changed.

Antonyms

• Reducible: Capable of being reduced.
• Simplifiable: Capable of being made simpler.
• Divisible: Capable of being divided.

Học thuật

Adjective

1. incapable of being made smaller or simpler
   • an irreducible minimum
   • an irreducible formula
   • an irreducible hernia