Interface Set<E>

All Known Subinterfaces:
AbelianGroup<E>, AbelianMonoid<E>, Algebra<E,F>, BanachAlgebra<E,F>, BanachSpace<E,S>, CStarAlgebra<E,F>, DivisionRing<E>, Field<E>, FiniteGroup<E>, FiniteSet<E>, GradedAlgebra<E,F>, Group<E>, HilbertSpace<E,S>, InfiniteSet<E>, KleeneAlgebra<E>, Lattice<E>, LieAlgebra<E,S>, Loop<E>, Magma<E>, Matrix<E>, MetricSpace<T>, Module<M,R>, Monoid<E>, NonAssociativeAlgebra<E,S>, OrderedGroup<E>, Quasigroup<E>, Ring<E>, SemiLattice<E>, Semiring<E>, SpacetimeMetric, TopologicalSpace<T>, Vector<E>, VectorSpace<V,F>
All Known Implementing Classes:
Boolean, BooleanAlgebra, Booleans, CliffordAlgebra, Complex, Complexes, CyclicGroup, DenseMatrix, DenseVector, DihedralGroup, DiscreteSet, DoubleField, FreeGroup, GenericMatrix, GenericVector, Integer, Integers, IntervalND, JuliaSet, KerrMetric, LieGroup, MandelbrotSet, MatrixLieAlgebra, MMapMatrix, NativeRealBig, NativeRealDoubleMatrix, NativeRealDoubleVector, NativeRealFloatMatrix, Natural, Naturals, Octonion, Octonions, Point2D, Point3D, PointND, PolynomialRing, Quaternion, QuaternionGroup, Quaternions, Rational, Rationals, Real, RealBig, RealDouble, RealDoubleMatrix, RealDoubleVector, RealFloat, RealFloatVector, Reals, SchwarzschildMetric, SIMDRealDoubleMatrix, SIMDRealFloatMatrix, SO3_1Group, SparseMatrix, SparseVector, SquareMatrices, SU2Group, SU3Group, SymmetricGroup, TiledMatrix, U1Group, Vector2D, Vector3D, Vector4D, VectorND, VectorSpace2D, VectorSpace3D
public interface Set<E>
Represents a mathematical set - a collection of distinct elements.

This is the foundational concept in mathematics. A set has no additional structure beyond membership. Higher-level structures (Magma, Group, Ring, Field) add operations and properties to sets.

Mathematical Definition

A set S is a well-defined collection of distinct objects, considered as a whole. The objects are called elements or members of the set.

Examples

  • â„• = {0, 1, 2, 3, ...} - Natural numbers
  • ℤ = {..., -2, -1, 0, 1, 2, ...} - Integers
  • ℝ - Real numbers
  • â„‚ - Complex numbers

Usage in Episteme

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Summary

    Modifier and Type
    Method
    Description
    boolean
    contains(E element)
    Tests whether this set contains the specified element.
    String
    description()
    Returns a human-readable description of this set.
    boolean
    isEmpty()
    Returns true if this set contains no elements.

  • Method Details

    • contains

      boolean contains(E element)
      Tests whether this set contains the specified element.

      This is the fundamental operation of a set - membership testing.

      Parameters:
      element - the element to test for membership
      Returns:
      true if this set contains the element, false otherwise
      Throws:
      NullPointerException - if the element is null and this set does not permit null elements
      See Also:

    • isEmpty

      boolean isEmpty()
      Returns true if this set contains no elements.

      The empty set (∅) is a fundamental concept in set theory. It is the unique set containing no elements.

      Returns:
      true if this set is empty

    • description

      String description()
      Returns a human-readable description of this set.

      Examples:

      • "ℝ (Real Numbers)"
      • "ℤ/12ℤ (Integers modulo 12)"
      • "{1, 2, 3, 4, 5}"

      Returns:
      a description of this set