Packages

case class furstenberg(k: Int) extends TacticsProof with PrimeDefinitions with Product with Serializable

Furstenberg's topological proof of the infinitude of primes.

furstenberg(k) proves that there are more than k primes.

Source
furstenberg.scala
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Inherited
  1. furstenberg
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
  6. PrimeDefinitions
  7. TacticsProof
  8. AnyRef
  9. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Instance Constructors

  1. new furstenberg(k: Int)

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from furstenberg to any2stringadd[furstenberg] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (furstenberg, B)
    Implicit
    This member is added by an implicit conversion from furstenberg to ArrowAssoc[furstenberg] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. val F: IndexedSeq[Const]
    Definition Classes
    PrimeDefinitions
  7. val FQ: LKProof
  8. val FR: LKProof
  9. val P: IndexedSeq[Const]
    Definition Classes
    PrimeDefinitions
  10. val Pi_1: LKProof
  11. val Q: IndexedSeq[Const]
    Definition Classes
    PrimeDefinitions
  12. val R: IndexedSeq[Const]
    Definition Classes
    PrimeDefinitions
  13. def RQ(n: Int): LKProof
  14. val S: IndexedSeq[Const]
    Definition Classes
    PrimeDefinitions
  15. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  16. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  17. val compCompProof: LKProof
  18. implicit def ctx: Context
    Definition Classes
    TacticsProof
  19. def ctx_=(newContext: Context): Unit
    Attributes
    protected
    Definition Classes
    TacticsProof
  20. val deMorgan1: LKProof
  21. def ensuring(cond: (furstenberg) ⇒ Boolean, msg: ⇒ Any): furstenberg
    Implicit
    This member is added by an implicit conversion from furstenberg to Ensuring[furstenberg] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: (furstenberg) ⇒ Boolean): furstenberg
    Implicit
    This member is added by an implicit conversion from furstenberg to Ensuring[furstenberg] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. def ensuring(cond: Boolean, msg: ⇒ Any): furstenberg
    Implicit
    This member is added by an implicit conversion from furstenberg to Ensuring[furstenberg] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  24. def ensuring(cond: Boolean): furstenberg
    Implicit
    This member is added by an implicit conversion from furstenberg to Ensuring[furstenberg] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  25. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  26. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  27. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from furstenberg to StringFormat[furstenberg] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  28. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  29. val infiniteSubset: LKProof
  30. val intersectionOpen: LKProof
  31. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  32. val k: Int
    Definition Classes
    furstenbergPrimeDefinitions
  33. def lambda(n: Int): LKProof
  34. def main(args: Array[String]): Unit
    Definition Classes
    TacticsProof
  35. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  36. final def notify(): Unit
    Definition Classes
    AnyRef
  37. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  38. val openClosedProof: LKProof
  39. val p: IndexedSeq[FOLConst]
    Definition Classes
    PrimeDefinitions
  40. val pgt0: LKProof
  41. val phi2: LKProof
  42. val prod: IndexedSeq[Const]
    Definition Classes
    PrimeDefinitions
  43. val progClosed: LKProof
  44. val proof: LKProof
  45. val psi1: LKProof
  46. val psi1Left: LKProof
  47. val psi1Right: LKProof
  48. val psi2: LKProof
  49. def psi2Right(n: Int): LKProof
  50. val singletonFinite: LKProof
  51. val singletonNonempty: LKProof
  52. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  53. val unionClosed: LKProof
  54. def varrho2(n: Int): LKProof

    Proof of x ∈ S[n] :- ∃y ( y ∈ P[n] ∧ x ∈ ν(0,y) )

  55. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  56. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  57. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  58. def [B](y: B): (furstenberg, B)
    Implicit
    This member is added by an implicit conversion from furstenberg to ArrowAssoc[furstenberg] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from PrimeDefinitions

Inherited from TacticsProof

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from furstenberg to any2stringadd[furstenberg]

Inherited by implicit conversion StringFormat from furstenberg to StringFormat[furstenberg]

Inherited by implicit conversion Ensuring from furstenberg to Ensuring[furstenberg]

Inherited by implicit conversion ArrowAssoc from furstenberg to ArrowAssoc[furstenberg]

Ungrouped