I am reading a math review in my thermodynamics text and I a little confused by this. Here is the excerpt: I am confused by the part where it says If they selected x = (y, z) then isn't that saying that x is dependent on y? So how can we just turn around and say y = y(x, z) ? That is, if we selected x as dependent in the first function, why can we turn around and call it independent in the second. Sorry, this might be a stupid question. I just don't see why we bother calling variables independent and dependent in a situation like this?