The number of elements in a [basis set](Vector%20spaces.md#Basis%20sets) that corresponds with a [vector space](Vector%20spaces.md) is the _dimension_, $n$ of the vector space (In this context we sometimes refer to this as the _Hamel dimension_). We say that an $n$ dimensional vector space (i.e. a [finite dimensional vector space](Finite%20dimensional%20vector%20spaces.md)) is defined over a field, $\mathbb{F}^n,$ and an [infinite dimensional vector space](Infinite%20dimensional%20vector%20spaces.md) is over $\mathbb{F}^\infty.$ ^58fc3e #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/VectorSpaces #MathematicalFoundations/Analysis/FunctionalAnalysis