This chapter starts with the counting or natural numbers, formalising them using structured types, thus allowing the definition of the standard numeric operators such as addition and multiplication. Using the natural numbers, the notions of mathematical and strong induction are formalised and illustrated through examples. Other classes of numbers, such as the integers, rational numbers and real numbers are also discussed. The notion of cardinality is presented, showing how one can reason about the size of finite, but also infinite sets.


Natural Number Prime Number Rational Number Proof Obligation Quotient Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gordon J. Pace
    • 1
  1. 1.Department of Computer Science, Faculty of Information and Communication TechnologyUniversity of MaltaMsidaMalta

Personalised recommendations