- Title Pages
- Preface
- Introduction
- I.1 About Choice
- I.2 Processes of Choice
- I.3 Democratic Choice
- I.4 Budget Allocation and Priority
- I.5 Ramsey's Savings Rule
- II.1 Utility Hypothesis
- II.2 Algebra of Revealed Preference
- II.3 Combinatorics of Demand
- II.4 Separable Utility
- II.5 Direct and Indirect Utility
- II.6 Efficiency and Inefficiency
- III.1 Price and Quantity Levels
- III.2 The True Index
- III.3 Fisher and Byushgens
- III.4 The Four‐Point Formula
- III.5 Wald's ‘New Formula’
- IV.1 Opportunity Models
- IV.2 Leontief's Input‐Output
- IV.3 The Market
- IV.4 Sraffa's Prices
- IV.5 General Economic Equilibrium
- IV.6 Von Neumann's Economic Model
- V.1 Optimal Programming
- V.2 Convex Programming
- V.3 Linear Programming
- V.4 Minimum Paths
- V.5 Distribution Matrices
- VI.1 Calculus of Propositions
- VI.2 Algebra of Relations
- VI.3 Intersections and Fixed Points
- Bibliography
- Index

# Algebra of Relations

# Algebra of Relations

- Chapter:
- (p.499) VI.2 Algebra of Relations
- Source:
- Logic of Choice and Economic Theory
- Author(s):
### S. N. Afriat

- Publisher:
- Oxford University Press

This is the second of three chapters on general mathematics as applied to economics, and presents a treatment of the algebra of relations. Relations are defined as subsets of a Cartesian product, or predicates involving several objects, so that Boolean theory (as described in the last chapter) applies to them. The five sections of the chapter are: operations with [binary] relations; classification of (binary) relations; order and equivalence; order refinement; and representation theorems.

*Keywords:*
algebra, binary relations, equivalence, mathematical economics, order, relations, representation theorems

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- Title Pages
- Preface
- Introduction
- I.1 About Choice
- I.2 Processes of Choice
- I.3 Democratic Choice
- I.4 Budget Allocation and Priority
- I.5 Ramsey's Savings Rule
- II.1 Utility Hypothesis
- II.2 Algebra of Revealed Preference
- II.3 Combinatorics of Demand
- II.4 Separable Utility
- II.5 Direct and Indirect Utility
- II.6 Efficiency and Inefficiency
- III.1 Price and Quantity Levels
- III.2 The True Index
- III.3 Fisher and Byushgens
- III.4 The Four‐Point Formula
- III.5 Wald's ‘New Formula’
- IV.1 Opportunity Models
- IV.2 Leontief's Input‐Output
- IV.3 The Market
- IV.4 Sraffa's Prices
- IV.5 General Economic Equilibrium
- IV.6 Von Neumann's Economic Model
- V.1 Optimal Programming
- V.2 Convex Programming
- V.3 Linear Programming
- V.4 Minimum Paths
- V.5 Distribution Matrices
- VI.1 Calculus of Propositions
- VI.2 Algebra of Relations
- VI.3 Intersections and Fixed Points
- Bibliography
- Index