If $X$ is distributed normally with mean $0$, is it correct to say $X$ and $-X$ "have the same distribution"? 
Q: If $X$ is distributed normally with mean $0$, is it correct to say $X$ and $-X$ have the same distribution?

In a way, this seems correct: both $X$ and $-X$ have the same probability density functions.  But, in other ways, it seems incorrect: (a) they're clearly not independent, and (b) $X \neq -X$, in general.
Is there a better way of phrasing this, both in this case, and in general (where $X$ and $f(X)$ have the same probability density functions)?  Or is the original phrasing acceptable?

Hint: Two random  variables $X,Y$ are equal in distribution if
$$
\mathbb{P}(X\leq z)=\mathbb{P}(Y\leq z) \, \mbox{for all } z.
$$
It doesn't have to do with independance either. Clearly $X$ and $X$ have the same distribution but$\ldots$
