This is the start of my course and this topic is kind of glossed over in an 'you should already know this' way, but I want to make sure I understand it.
In 3D space, what is the dimension of the set of points that simultaneously satisfy the two equations
(a) x+y=3 and (b) z^2=x^2+y^2
My answer would be that (a) has one dimension because we only need either x or y in order to determine the point. Similarly, (b) needs any 2 of the 3 variables in order to define the missing one, so its dimension is 2? If that is the case, then to simultaneously satisfy both it must have 2 dimensions?