### Definition of Irreducible

1. Adjective. Incapable of being made smaller or simpler. "An irreducible hernia"

Antonyms: Reducible

### Definition of Irreducible

1. a. Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia.

### Definition of Irreducible

1. Adjective. Not able to be reduced or lessened. ¹

2. Adjective. Not able to be brought to a simpler or reduced form. ¹

3. Adjective. (mathematics of a polynomial) Unable to be factorized into polynomials of lower degree, as ''(x^2 + 1)''. ¹

4. Adjective. (mathematics of an integer) Unable to be factored into smaller integers; prime. ¹

5. Adjective. (topology of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball. ¹

6. Adjective. (group theory of a representation) impossible to divide further into representations of lower dimension by means of any similarity transformation ¹

7. Noun. (mathematics) Such a polynomial ¹

¹ Source: wiktionary.com

### Medical Definition of Irreducible

1. 1. Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia. 2. Incapable of being reduced to a simpler form of expression; as, an irreducible formula. Irreducible case, a particular case in the solution of a cubic equation, in which the formula commonly employed contains an imaginary quantity, and therefore fails in its application. Irredu"cibleness, Irredu"cibly. Source: Websters Dictionary (01 Mar 1998)

### Irreducible Pictures

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### Lexicographical Neighbors of Irreducible

 irrecuredirrecusableirrecusablyirredeemabilityirredeemableirredeemablenessirredeemablyirredentairredentasirredentism irredentismsirredentistirredentistsirreducibilitiesirreducibilityirreducible (current term)irreducible complexityirreducible herniairreduciblenessirreducibles irreduciblyirredundantirreferentialirreflectionirreflectiveirreflexiveirreformabilityirreformableirrefragabilityirrefragable

### Literary usage of Irreducible

Below you will find example usage of this term as found in modern and/or classical literature:

1. Theory of Functions of a Complex Variable by Andrew Russell Forsyth (1893)
"The representation of any compound circuit in terms of a system of independent irreducible circuits is unique: if there were two different expressions, ..."

2. Theory of Functions of a Complex Variable by Andrew Russell Forsyth (1893)
"The representation of any compound circuit in terms of a system of independent irreducible circuits is unique: if there were two different expressions, ..."

3. The Encyclopædia Britannica: A Dictionary of Arts, Sciences, Literature and by Hugh Chisholm (1910)
"It is proper to refer also to Abel's definition of an irreducible equation : — an equation \$x »o. the coefficients of which are rational functions of a ..."

4. Proceedings of the Royal Society of London by Royal Society (Great Britain) (1904)
"Mr. JH Grace, in a note appended to the paper, has deduced from this result a means of calculating the maximum order, in the variables, of an irreducible ..."

5. The Encyclopædia Britannica: A Dictionary of Arts, Sciences, Literature and by Hugh Chisholm (1910)
"It is proper to refer also to Abel's definition of an irreducible equation : — an equation \$x »o. the coefficients of which are rational functions of a ..."

6. Proceedings of the Royal Society of London by Royal Society (Great Britain) (1904)
"Mr. JH Grace, in a note appended to the paper, has deduced from this result a means of calculating the maximum order, in the variables, of an irreducible ..."

7. The Collected Mathematical Papers of Arthur Cayley by Arthur Cayley (1889)
"the numerator is equal to where the series of factors does not terminate ; hence [incorrect, see p. 253] the number of irreducible invariants is infinite ..."

8. The American Journal of the Medical Sciences by Southern Society for Clinical Investigation (U.S.) (1890)
"THE OPERATIVE TREATMENT OF DISLOCATIONS irreducible BY ORDINARY MEANS. Several cases of dislocation which could be reduced only by operation, are reported ..."

9. The Collected Mathematical Papers of Arthur Cayley by Arthur Cayley (1889)
"the numerator is equal to where the series of factors does not terminate ; hence [incorrect, see p. 253] the number of irreducible invariants is infinite ..."

10. The American Journal of the Medical Sciences by Southern Society for Clinical Investigation (U.S.) (1890)
"THE OPERATIVE TREATMENT OF DISLOCATIONS irreducible BY ORDINARY MEANS. Several cases of dislocation which could be reduced only by operation, are reported ..."

11. Unemployment: A Problem of Industry by William Henry Beveridge Beveridge (1912)
"Constitution of irreducible minimum shown by distribution of unemployment ... irreducible minimum only a sample of irregular reserves of casual employment. ..."

12. Unemployment: A Problem of Industry by William Henry Beveridge Beveridge (1912)
"Constitution of irreducible minimum shown by distribution of unemployment ... irreducible minimum only a sample of irregular reserves of casual employment. ..."