definition of well ordered set, a variant
It is possible to define well-ordered sets as follows:
a well-ordered set is a partially ordered set in which every nonempty subset of has a least member.
To justify the alternative, we prove that every partially ordered set in which every nonempty subset has a least member is total:
The alternative has the benefit of being a stronger statement in the sense that
given that every nonempty subset has a least member.
- 1 Schechter, E., Handbook of Analysis and Its Foundations, 1st ed., Academic Press, 1997.
- 2 Jech, T., Set Theory, 3rd millennium ed., Springer, 2002.
|Title||definition of well ordered set, a variant|
|Date of creation||2013-03-22 18:04:47|
|Last modified on||2013-03-22 18:04:47|
|Last modified by||yesitis (13730)|