Encyclopedia Britannica
Encyclopedia Britannica
SUBSCRIBE
SUBSCRIBE
SUBSCRIBE TO PREMIUM
  • Home
  • Biographies
  • Animals & Nature
  • History & Society
  • Science & Tech
  • Geography & Travel
  • Arts & Culture
  • ProCon
  • Money
  • Games & Quizzes
  • Videos
  • Today in History
  • Dictionary
  • New Articles
Biographies
  • Browse Biographies
Animals & Nature
  • Birds, Reptiles & Other Vertebrates
  • Environment
  • Fossils & Geologic Time
  • Insects & Other Invertebrates
  • Mammals
  • Plants
History & Society
  • History
  • Philosophy & Religion
  • Politics, Law & Government
  • Society & Social Issues
Science & Tech
  • Health & Medicine
  • Science
  • Technology
Geography & Travel
  • Geography & Travel
Arts & Culture
  • Entertainment & Pop Culture
  • Literature
  • Sports & Recreation
  • Visual Arts
  • Image Galleries
  • Podcasts
  • Summaries
  • Top Questions
  • Lists and Stories
  • Britannica Kids
Ask the Chatbot Games & Quizzes History & Society Science & Tech Biographies Animals & Nature Geography & Travel Arts & Culture ProCon Money Videos
completeness
References
Britannica AI Icon

completeness

mathematics
Written by
The Information Architects of Encyclopaedia Britannica

The Information Architects maintain a master list of the topics included in the corpus of  Encyclopædia Britannica, and create and manage the relationships between them.

The Information Architects of Encyclopaedia Britannica

Learn about this topic in these articles:

  • real number

    …the important mathematical property of completeness, meaning that every nonempty set that has an upper bound has a smallest such bound, a property not possessed by the rational numbers. For example, the set of all rational numbers the squares of which are less than 2 has no smallest upper bound,…

    Read More

    …the important mathematical property of completeness, meaning that every nonempty set that has an upper bound has a smallest such bound, a property not possessed by the rational numbers. For example, the set of all rational numbers the squares of which are less than 2 has no smallest upper bound,…

    Read More
  • transformation of a circular region into an approximately rectangular region
    analysis
    / Properties of the real numbers

    …captured by the concept of completeness.

    Read More

    …captured by the concept of completeness.

    Read More