Linear Independence of Vectors Spanning $\mathbb{R}^n$

[Dustinsfl]

If x₁, x₂,..., x_n span $\mathbb{R}^n$, then they are linearly independent.

This is true since n-1 vectors can't span R^n.

How can this be written in a more meaningful way?

 

[Squeezebox]

$\mathbb{R}^n$ is an n-dimensional vector space. {x₁,x₂,...,x_n} is a spanning set of $\mathbb{R}^n$ of length n. This makes {x₁,x₂,...,x_n} a basis of $\mathbb{R}^n$, which means it must be linearly independent.