Least Upper Bound Property/Also known as

Least Upper Bound Property: Also known as

The least upper bound property of $\R$ is also known as:

the supremum principle
the completeness property
the continuum property (although this is also used to encompass the Greatest Lower Bound Property, a complementary result).


Sources

  • 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $1$: Review of some real analysis: $\S 1.1$: Real Numbers: Axiom $1.1.4$
  • 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: $\S 2.4$: The Continuum Property
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): order properties (of real numbers): $(5)$: Completeness property
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): order properties (of real numbers): $(5)$: Completeness property
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): bound
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.