The Vapnik-Chervonenkis dimension or VC-dimension of a nonempty concept class 
is the cardinal number
of the largest finite set 
which can be shattered by 
. If arbitrarily large finite sets
can be shattered by 
, then the VC-dimension is said to be 
. Given a concept class 
,
the VC-dimension of 
is sometimes denoted 
.
Examples of concept classes used to study the Vapnik-Chervonenkis dimension include families of intervals (and unions thereof) on the real line, rectangles and squares in the plane, and hyperplanes.
There are also several results quantifying the VC-dimension to various degrees. For example, one can show that the VC-dimension of a nonempty finite concept class 
satisfies
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