How can I write that a point in space is found within a unit sphere?

Question

I have a point $a$, with coordinates $(x,y,z)$ and I want to write, using set builder notation, that this point is found within the unit sphere $1=x^2 + y^2 + z^2$. How could I formulate this?

Answer 1

Almost exactly how you phrased it.

$$a\in\{(x,y,z)\in\mathbb{R}^3\;|\; x^2+y^2+z^2\leq1\}$$