irreducibility Definition
- 1the quality or state of being impossible to reduce or simplify
- 2the quality or state of being irreducible
Using irreducibility: Examples
Take a moment to familiarize yourself with how "irreducibility" can be used in various situations through the following examples!
Example
The irreducibility of the problem made it difficult to solve.
Example
The irreducibility of the concept was a source of frustration for the students.
irreducibility Synonyms and Antonyms
Synonyms for irreducibility
- incompressibility
- indivisibility
- unreducibility
Phrases with irreducibility
irreducibility of polynomials
the property of a polynomial that cannot be factored into polynomials of lower degree over the same field
Example
The irreducibility of the polynomial x^2 + 1 over the real numbers is well-known.
irreducibility of representations
the property of a representation of a group that cannot be decomposed into smaller, simpler representations
Example
The irreducibility of the representation of the symmetric group on n letters is a fundamental result in algebraic combinatorics.
the property of a problem or system that cannot be reduced to a simpler or more efficient form without loss of information or functionality
Example
The irreducibility of the complexity of the human brain is a major challenge for neuroscience.
Summary: irreducibility in Brief
The term 'irreducibility' [ˌɪrɪˌdʌsəˈbɪlɪti] refers to the quality or state of being impossible to reduce or simplify. It can apply to problems, concepts, or representations, as in 'The irreducibility of the problem made it difficult to solve.' 'Irreducibility' extends into phrases like 'irreducibility of polynomials,' and implies the property of a polynomial that cannot be factored into polynomials of lower degree over the same field.
