Numbers

RISC-Linz logo

Wolfgang Schreiner
Research Institute for Symbolic Computation (RISC-Linz)
Johannes Kepler University, Linz, Austria
  • Overview
  • Natural Numbers
  • Peano Arithmetic
  • Illustration
  • Construction from Sets
  • Set of Natural Numbers
  • Auxiliary Notions
  • Natural Number Arithmetic
  • Example
  • Natural Number Laws
  • Natural Number Laws
  • Order Predicates
  • Logic Evaluator
  • Difference
  • Quotient and Remainder
  • Properties of Quotient and Remainder
  • Exponentiation
  • More Notions
  • Examples
  • More Notions
  • Logic Evaluator
  • Motivation
  • Definition
  • Example
  • Integer Arithmetic
  • Examples
  • More Arithmetic
  • Integer Laws
  • Difference
  • Proof (Continued)
  • Integer Numbers
  • Motivation
  • Definition
  • Constructor function
  • Numerator and Denominator
  • Rational Arithmetic
  • Quotient
  • Rational Numbers
  • Motivation
  • Theory of Reals
  • Existence of Real Roots
  • Real Numbers
  • Motivation
  • Definition
  • Complex Number Operations
  • Example
  • Fundamental Theorem of Algebra
  • Complex Square Root
  • Complex Conjugate
  • Complex Numbers
  • Relationship between Number Domains
  • Minimum and Maximum Quantifier
  • Minimum and Maximum Function
  • Sum Quantifier
  • Examples
  • Examples
  • Example: Decimal Number Representation
  • Example: Binary Number Representation
  • Multiple Variable Bindings
  • Sum Identities
  • Sum Identities
  • Examples
  • Product Quantifier
  • Example
  • Product Identities
  • Factorial
  • Binomial
  • Motivation
  • Binomial Identities
  • Pascal's Triangle
  • Construction
  • Matrix Operations
  • Polynomials
  • Special Polynomials
  • Polynomial Operations
  • Examples
  • Relationship to Reals
  • Polynomial Evaluation
  • Polynomial Evaluation
  • Typical Notation
  • Summary

  • Author: Wolfgang Schreiner
    Last Modification: November 16, 1999

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