Why prior in MAP could be ignored? A posterior  $p(\theta\vert x) = \frac{p(x \vert \theta)p(\theta)}{p(x)} $

Many materials say that since the $p(x)$ is a constant, the $p(x)$ can be ignored. Thus, $p(\theta\vert x) \propto p(x \vert \theta)p(\theta)$ 

My question is why $p(x)$ is a constant and ignored. Is this because even though we don't know the distribution x, there is a corresponding true distribution for $x$? So, $p(x) $ is a constant (we don't know but already determined) and thus, can be ignored?
The maximum a posteriori definition usually goes like this:

$$ \arg\max_{\theta} p(\theta|x) = \arg\max_{\theta} \frac{p(x|\theta)\cdot p(\theta)}{p(x)} $$

and given that $p(x)$ is independent of $\theta$, it's not needed for finding the $\arg\max_{\theta}$, then you have 

$$ \arg\max_{\theta} p(\theta|x) = \arg\max_{\theta} \frac{p(x|\theta)\cdot p(\theta)}{p(x)} =  \arg\max_{\theta} p(x|\theta)\cdot p(\theta)$$