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What does irreducibility mean?

Looking for the meaning or definition of the word irreducibility? Here's what it means.

Noun
  1. (uncountable) The quality or degree of being irreducible.
  2. (countable) Something that is irreducible.
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Examples
Irreducibility can be characterized by saying that all the projects are linked together, both forwards and backwards.
In fact, the poet depends on the irreducibility of such cognitively significant meanings in order for him to be creative.
It is the characters' many-sidedness, their irreducibility to a formula, that he believes accounts for readers' continuing delight in Joyce's narrative.
His images, like Celan's, are concentrated to the point of irreducibility.
In addition, she rightly admits the inherent irreducibility of all media.
This paper studies analytic maps between free spectrahedra, and under certain irreducibility assumptions on the convex sets, classifies all those that are bianalytic.

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