How Many Movable Ways(vector) In Pure $N$th-Dimensional Space? !enter image description here In my opinion, In pure $2$th-dimensional space, There is 2 movable ways. !enter image description here And in pure $3$th-dimensional space, There is 3 movable ways. Am I think in right way? Any answers will be appreciated, thank you. **Added.** Here is what I'm thinking about "Real Space" !enter image description here Two dots are particles.(such as electron) The lines which they release is quantized. So it can be measurable or comparable distance between two dots.

In $N$ dimensional space there are $N$ basis vectors, and hence $N$ "directions".