Etymology
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irreducible (adj.)

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

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Definitions of irreducible

irreducible (adj.)
incapable of being made smaller or simpler;
an irreducible formula
an irreducible minimum
an irreducible hernia
From wordnet.princeton.edu