Very simple question about signal periodicity $$x[n] = u[n]+u[-n]$$

Is it periodic or not? My answer is  

$$u[n] = {1       , n\geqslant0}$$
$$u[-n] = {1      , n\leqslant0}$$

which means that the signal $x[n]$ is always equal to $1$ from $-\infty$ to $+\infty$, but it equals $2$ at $n=0$. Am I right?
no, but $x[n]$ is, what we call, an "even-symmetry" function:

$$ x[-n] = x[n] \quad \forall n \in \mathbb{Z} \ . $$

what makes $x[n]$ periodic is $$ x[n+N] = x[n] \quad \forall n \in \mathbb{Z} $$ which is really the premise for the DFT of length $N$.