Definition:Dedekind Completeness Property/Also known as
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Dedekind Completeness Property: Also known as
The Dedekind completeness property is commonly referred to as:
- the supremum property
- the least upper bound property
- the infimum property
- the greatest lower bound property
- the completeness property
where the latter denominations are justified by Dedekind Completeness is Self-Dual.
A set which fulfils the Dedekind completeness property is described as being Dedekind complete.
Some sources hyphenate: Dedekind-complete.
In the interest of consistency, $\mathsf{Pr} \infty \mathsf{fWiki}$ prefers the non-hyphenated version.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Dedekind-complete
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): completeness property
- 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 3$: Relations
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): completeness property