- #1
Simfish
Gold Member
- 823
- 2
So here are some functions of the following types...
f: R -> R^2 (curves in the plane)
f: R -> R^3 (curves in space)
f: R^2 -> R (functions f(x,y) of 2 vars)
f: R^3 -> R: (functions f(x,y,z) of 3 vars)
f: R^2 -> R^2 (vector fields v(x,y) in the plane)
The question is - why are curves in the plane of the form R -> R^2? My intuition tells me R^2 -> R^2 (since after all, curves in the plane are based on x and y coordinates...). And R^2 is a cartesian product of two sets. For any curve, I'd expect x AND y input values...
f: R -> R^2 (curves in the plane)
f: R -> R^3 (curves in space)
f: R^2 -> R (functions f(x,y) of 2 vars)
f: R^3 -> R: (functions f(x,y,z) of 3 vars)
f: R^2 -> R^2 (vector fields v(x,y) in the plane)
The question is - why are curves in the plane of the form R -> R^2? My intuition tells me R^2 -> R^2 (since after all, curves in the plane are based on x and y coordinates...). And R^2 is a cartesian product of two sets. For any curve, I'd expect x AND y input values...