The well ordering principle states that every nonempty set of positive integers contains a smallest member.
The well ordering theorem instead asserts the existence of a well order on an arbitrary set.
Well Ordering Principle
See also
Well Ordered Set, Well Ordering TheoremExplore with Wolfram|Alpha
References
Apostol, T. M. "The Well-Ordering Principle." §I 4.3 in Calculus, 2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. Waltham, MA: Blaisdell, pp. 34-35, 1967.Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 149, 1993.Referenced on Wolfram|Alpha
Well Ordering PrincipleCite this as:
Weisstein, Eric W. "Well Ordering Principle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WellOrderingPrinciple.html