Let $V$ be a vector space in $F$, and suppose that $V$ has a finite spanning set $S=\{v_1,\ldots,v_n\}$. Show that if $T=\{u_1,\ldots,u_m\}$ is a linearly independent subset of V, then $m\leq n$. (We are not assuming $T$ is a subset of $S$)
I have tried going about this using contradiction, but I'm unclear as to whether that is enough or how to start from there. Thanks in advance