$\underline {Background}$:Let,$E$ be a coherent sheaf on a Noetherian,integral scheme $X$ and $\dim E$=$\dim X$.
Then we have the unique torsion filtration of that coherent sheaf as
$0\subset T_0(E)\subset....\subset T_{\dim X-1}(E) \subset T_{\dim X} (E)=E$
where,$T_i(E)$ is the maximal subsheaf of of $E$ of dimension $\leq i$
we also have torsion subsheaf of $E$ ,denoted by $T(E)$ which is defined as
for any affine $SpecA$ in $X$, define $ T(E)(SpecA)$:={$m \in E(SpecA)|\exists s\in A$ with $s$ nonzero such that $s.m=0$}
we also have $(T(E))_x=T(E_x)$
$\underline {Question}$:How do we show that $T(E)=T_{\dim X-1}(E)$
I only know that $T(E)$ is a subsheaf of $E$ ,and I am supposed to show the following
$T(E)$ is a maximal subsheaf of dimension $\leq \dim(X)-1$.
I have no clue how to show (i) it has dimension $\leq \dim(X)-1$ and
(ii) It is maximal among all such subsheaves.
Any help from anyone is welcome.