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?

Since $X$ has a normal distribution, which is symmetric around its mean, then yes, $X$ and $-X$ have the same distribution.
For example, if $X \sim N(0,17)$, then $-X \sim N(0,17)$.
In addition, $X$ and $-X$ are negatively correlated, since $-X = -x$ when $X = x$.
But two identically distributed variables can still be correlated, so that's OK.
