Can an x value in a Bernoulli distribution take on any other value than 0 or 1?

Question

I am puzzling over the parametric statement for the Bernoulli Distribution

$p(x \vert \theta) = \theta^x(1-\theta)^(1-x)$

Can X take on other values than 1 and zero?

Answer 1

$x$ can only take the values of $0$ and $1$.

But that does not mean that $p(x|\theta)$ is $1$...