The maximum cardinal number of a collection of subsets of a 
-element set 
, none of which contains another, is the binomial
coefficient 
,
where 
is the floor function.
Sperner's Theorem
See also
Cardinal Number, Sperner's LemmaExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Sperner's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpernersTheorem.html