Compendium of Predicates
  • 🌐Orientation
    • ⭐Welcome
    • āœ’ļøNotation
    • šŸ˜…An Example
  • 🧰Definitions
    • Relation Taxonomy
    • Order Taxonomy
    • Algebra
      • Magma
      • Semigroup
      • Monoid
      • Group
      • Ringoid
      • Semiring
      • Ring
      • Unit Ring
      • Boolean Ring
      • Boolean Group
    • Bandler and Kohout Products of Relations
    • Closed
    • Complement
    • De Baets and Kerre Products of Relations
    • Extremal Elements
    • Galois Connection
    • Images of a set under a relation
    • Indexed Union and Intersection
    • Monoidal Preorder
    • Monotone Map
    • Natural Projection
    • Non-Preservation of Extrema
    • Over and Under
    • Power Set
    • Preorder
    • Preservation of Extrema
    • Product
    • Relation Inclusion
    • Row Constant Relations
    • Semilattice
    • Set Inclusion
    • Symmetric Monoidal Preorder
    • Upper Set
  • šŸ”¬Checks
    • šŸŽ™ļøA few words about the checks
    • Indirect Equality and Inclusion
    • Below
    • Extremal Elements
    • Relation Division
    • Algebra
      • Ring
      • Boolean Ring
      • Boolean Group
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  1. Definitions

Row Constant Relations

Better known as Vectors and Points

PreviousRelation InclusionNextSemilattice

Last updated 1 year ago

RowConstantā€…ā€ŠAā€…ā€ŠBā€…ā€ŠR\textbf{RowConstant} \; A \; B \; RRowConstantABR

Relationā€…ā€ŠAā€…ā€ŠBā€…ā€ŠR\textbf{Relation} \; A \; B \; RRelationABR


pred RowConstant(A,B,C: set univ, R: univ->univ) {
  Relation[A,B,R]
  R = R.(B->C)
}
Pointā€…ā€ŠAā€…ā€ŠBā€…ā€ŠR\textbf{Point} \; A \; B \; RPointABR

RowConstantā€…ā€ŠAā€…ā€ŠBā€…ā€ŠR\textbf{RowConstant} \; A \; B \; RRowConstantABR

Injectiveā€…ā€ŠAā€…ā€ŠBā€…ā€ŠR\textbf{Injective} \; A \; B \; RInjectiveABR

Surjectiveā€…ā€ŠAā€…ā€ŠBā€…ā€ŠR\textbf{Surjective} \; A \; B \; RSurjectiveABR


pred Point(A,B: set univ, R: univ->univ) {
  RowConstant[A,B,B,R]
  Injective[A,B,R]
  Surjective[A,B,R]
}
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