Why the notion of degree of freedom is correct?

The intuitional definition for number of degrees of freedom is following: it is the minimal amount of numbers which allows us to describe the system's configuration correctly.

For example, for dot in our space it is enough to set 3 real numbers. But we know, that the line of real numbers is isomorphic to 3D space, so we could desribe the place of a dot using only one number with this isomorphism!

So, how does it comply with the fact, that a dot has 3 degrees of freedom?

• – leonbloy Feb 20 '19 at 19:21
• There is no recursive isomorphic mapping from the line to 3d space, no algorithm to get one from the other. – Wolphram jonny Feb 20 '19 at 21:59