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In mathematics, the idea of '''irreducibility''' plays a fundamental role. It concerns objects which cannot be broken down into simpler objects of the same kind. Mathematicians then focus their research on these "simplest" objects, the irreducibles. For example irreducible numbers are [[Prime_number|prime]], the building blocks of all other numbers.  

In mathematics, the idea of '''irreducibility''' plays a fundamental role. It concerns objects which cannot be broken down into simpler objects of the same kind. Mathematicians then focus their research on these "simplest" objects, the irreducibles. For example irreducible numbers are [[Prime_number|prime]], the building blocks of all other numbers.  

Each of the following objects, sampled from across mathematical disciplines, has an irreducible version: [[Number|numbers]], [[Polynomial|polynomials]], [[Algebraic_variety|algebraic varieties]], [[Cantor_set|Cantor sets]], [[Algebraic_curve|algebraic curves]], [[Lattice| lattices]], non-deterministic [[Set|sets]], [[Topology|topological spaces]], [[Hyperbolic_geometry|hyperbolic geometries]], [[Simplex|simplices]] (simplexes), [[Polyhedron|polyhedra]], [[Contour_integral|contour integrals]], and [[Harmonic_series|harmonic series]].

Each of the following objects, sampled from across mathematical disciplines, has an irreducible version: [[Number]]s, [[polynomial]]s, [[Algebraic_variety|algebraic varieties]], [[Cantor set]]s, [[algebraic curve]]s, [[lattice]]s, non-deterministic [[set]]s, [[Topology|topological spaces]], [[Hyperbolic_geometry|hyperbolic geometries]], [[Simplex|simplices]] (simplexes), [[Polyhedron|polyhedra]], [[contour integral]]s, and [[harmonic series]].

[[Category:Mathematics]]

[[Category:Mathematics]]