A set partition of the rational numbers into two nonempty subsets 
and 
such that all members of 
are less than those of 
and such that 
has no greatest member. Real
numbers can be defined using either Dedekind cuts or Cauchy
sequences.
Dedekind Cut
See also
Cantor-Dedekind Axiom, Cauchy SequenceExplore with Wolfram|Alpha
References
Courant, R. and Robbins, H. "Alternative Methods of Defining Irrational Numbers. Dedekind Cuts." §2.2.6 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 71-72, 1996.Jeffreys, H. and Jeffreys, B. S. "Nests of Intervals: Dedekind Section." §1.031 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 6-8, 1988.Referenced on Wolfram|Alpha
Dedekind CutCite this as:
Weisstein, Eric W. "Dedekind Cut." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DedekindCut.html