Convention for 2-Space and 3-Space

Question

I am curious by this following symbol which I see on the Math.SE alot which is the following:

$$\mathbb{R}^2 \ \mathrm{or} \ \mathbb{R}^3$$

This this a convention to write 2-space or all reals 2-space, and respectively all reals 3-space? I am currently in calculus, was wondering what the convention represents.

Answer 1

For the record, here's a precise definition: $$\Bbb R^n = \{ (x_1,\ldots, x_n) \mid x_i \in \Bbb R \mbox{ for all }i=1,\ldots,n \}.$$For $n=2$ and $n=3$ you have $$\Bbb R^2 = \{(x,y) \mid x,y \in \Bbb R\} \quad\mbox{and}\quad \Bbb R^3 = \{(x,y,z) \mid x,y,z \in \Bbb R\}.$$