# Dimensionality

The dimension is the number of vectors in a basis.

For infinite dimensional spaces, if you have an infinite set of linearly independent vectors then they might not span the entire space.

## Definition

The dimension of a vector space is defined as the number of vectors in its basis (linearly independent set that spans the space). In other words, it is the maximum number of linearly independent vectors in a space. (Finite, countably infinite, uncountably infinite)