There is a theorem that states: $$Let \space S=\{v\_1,v\_2,...v\_r\}\space be \space a \space set \space of\space vectors \space in\space \mathbb{R}^n. \space If\space r>n,\space then\space S\space is\space linearly\space dependent.$$ My question is, does the 'other' case apply as well? By other case, I mean if $r<n$, does this mean the set $S$ is linearly independent or linearly dependent? No proofs please, just some intuition behind the answer if possible! 

Thanks in advance!