Every real number is negative, 0, or positive. The law is sometimes stated as "For
arbitrary real numbers 
and 
,
exactly one of the relations 
, 
, 
holds" (Apostol 1967, p. 20).
Trichotomy Law
See also
Schröder-Bernstein Theorem, Total OrderExplore with Wolfram|Alpha
References
Apostol, T. M. Calculus, 2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. Waltham, MA: Blaisdell, 1967.Referenced on Wolfram|Alpha
Trichotomy LawCite this as:
Weisstein, Eric W. "Trichotomy Law." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TrichotomyLaw.html