1. The problem statement, all variables and given/known data Let V be a finite dimensional subspace. Let V[tex]\supseteq[/tex]U1[tex]\supseteq[/tex]U2[tex]\supseteq[/tex]...[tex]\supseteq[/tex]Uk. Show that there exists k such that Uk=Uk+1=...=Un=... 2. Relevant equations We were also told to assume none of the subspaces are zero dimensional, and to think about how the dimensions can change throughout. 3. The attempt at a solution I know that all the Ui's are closed under vector addition, but I really don't know what to do with the information. I really don't know where to start. Any and all help will be appreciated. Thanks guys.