definitions
• synonyms

# irreducible

[ir-i-doo-suh-buh l, -dyoo-]
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1. not reducible; incapable of being reduced or of being diminished or simplified further: the irreducible minimum.
2. incapable of being brought into a different condition or form.
3. Mathematics.
1. of or relating to a polynomial that cannot be factored.
2. of or relating to a group that cannot be written as the direct product of two of its subgroups.

## Origin of .css-1fxfie5{font-size:22px;}@media (max-width:768px){.css-1fxfie5{font-size:18px;margin:0 10px 10px 0;word-break:break-all;word-wrap:break-word;-webkit-hyphens:auto;-moz-hyphens:auto;-ms-hyphens:auto;hyphens:auto;line-height:22px;}}irreducible

First recorded in 1625–35; ir-2 + reducible
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## Examples from the Web for irreducible

### Historical Examples

• #### The one-third of the French law seemed to be the irreducible minimum.

Notes on Life and Letters

• #### It is an irreducible minimum in connection with the Reward System.

British Dictionary definitions for irreducible

# irreducible

1. not able to be reduced or lessened
2. not able to be brought to a simpler or reduced form
3. maths
1. (of a polynomial) unable to be factorized into polynomials of lower degree, as (x ² + 1)
2. (of a radical) incapable of being reduced to a rational expression, as √(x + 1)
Derived Formsirreducibility or irreducibleness, nounirreducibly, adverb
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Word Origin and History forirreducible

1530s, from assimilated form of in- (1) "not, opposite of" + reducible. Related: Irreducibly; irreducibility.