Show how two sets are equinumerous. The following is a question from a textbook for one of my university classes called computational logic. The class is actually being offered as a philosophy class and since I have no real mathematical background I don't really know how to proceed. any help would be appreciated.
"Show that the set of real numbers is equinumerous with the the set of points on a semicircle from a circle with a diameter of 1."
EDIT: I can now add that the semicircle given in the diagram that accompanied the question is the bottom half of the circle described by $0.25=(x-0.5)^2+(y-0.5)^2$. though I dont know if that really matters.

HINT: Assuming that it’s an open semicircle (i.e., one that does not include its endpoints), let the semicircle be the set of points on the circle $x^2+(y-1)^2=1$ with $y$-coordinate less than $1$, and map each point to its projection on the $x$-axis when the centre of projection is the point $\langle 0,1\rangle$.
