ir·​re·​duc·​ible ˌir-i-ˈdü-sə-bəl How to pronounce irreducible (audio)
: impossible to transform into or restore to a desired or simpler condition
an irreducible matrix
specifically : incapable of being factored into polynomials of lower degree with coefficients in some given field (such as the rational numbers) or integral domain (such as the integers)
an irreducible equation
: impossible to make less or smaller
an irreducible minimum
irreducibility noun
irreducibly adverb

Examples of irreducible in a Sentence

They thought the world was made up of four irreducible elements: earth, air, fire, and water.
Recent Examples on the Web These smaller polynomials, known as irreducible polynomials, are the prime numbers of the polynomial world. Kevin Hartnett, Quanta Magazine, 6 May 2024 Advertisement Books Los Angeles is refracted in all its irreducible, unexplainable glory in ‘Dear Los Angeles’ Nov. 30, 2018 That said, this collection — at least chronologically — comes second. David Kipen, Los Angeles Times, 29 Sep. 2023 Klay is sensitive to the irreducible gap between the fewer than one percent of Americans who served in Afghanistan and Iraq and the 99 percent who did not. Phil Klay, Foreign Affairs, 18 Apr. 2023 An irreducible polynomial — one that can’t be factored — is the analogue of a prime number. Alex Stone, Quanta Magazine, 5 June 2023 There’s a gap — or a lag, maybe — between how new technologies can reduce our personhood to data, and the irreducible facts of our bodies, our health, our need to eat and sleep. Emma Goldberg, New York Times, 28 Apr. 2023 The irreducible fact, said Annabel Thomas, founder of Nc’nean distillery, is that some kind of fuel has to boil the mash and distill the alcohol. William Booth, Washington Post, 23 Mar. 2023 There is real pain and irreducible violence in the music. Chris Wheatley, Longreads, 31 July 2022 The thing is defiantly irreducible, because its aims are simple and direct. Vulture, 4 Apr. 2023

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'irreducible.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

First Known Use

1633, in the meaning defined at sense 1

Time Traveler
The first known use of irreducible was in 1633

Dictionary Entries Near irreducible

Cite this Entry

“Irreducible.” Dictionary, Merriam-Webster, Accessed 24 May. 2024.

Kids Definition


ir·​re·​duc·​ible ˌir-i-ˈd(y)ü-sə-bəl How to pronounce irreducible (audio)
: not reducible
irreducibility noun
irreducibly adverb

Medical Definition


ir·​re·​duc·​ible ˌir-i-ˈd(y)ü-sə-bəl How to pronounce irreducible (audio)
: impossible to bring into a desired or normal state
an irreducible hernia
irreducibility noun
plural irreducibilities

More from Merriam-Webster on irreducible

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