Hello im studying special relativity and i was wondering something about length contraction. Let's say someone who is not moving is seeing a rod which has one edge at $x=0$ and the other at $x=a$ so its length is $a$. An observer moving at constant speed $u$ along the $x$-axis uses lorentz transformation to determine the coordinates of these two points in his frame of refrence.
$x'_a=\gamma(a-ut)$, $x'_0=\gamma(0-ut)$ so to find the length of the rod we take the difference of these two points and it gives us $x'_a-x'_0=\gamma a$
I know that $\gamma>1$ so shouldn't the moving reference frame observe the rod to be bigger? Why are we talking about length contraction? I know something is wrong the way i derived this so can anyone explain to me where my mistake lies?