Cardinality of Two Sets of Points The problem is stated-
Do the following two sets of points have the same cardinality and if so, establish a bijection:
A line segment of length four and half of the circumference of radius one (including both endpoints).
My reasoning is they do have the same cardinality and my bijection is a picture in which I drew a horizontal line and a semicircle under it  (separated by approx. 2cm with the semicircle's open side facing down).  At what would be the center of the circle made by the semi-circle I drew a point P.  I then drew lines vertical from the original horizontal line to point P.  This shows, goes my reasoning, that for every point on the line there is a corresponding point on the semi-circle.
My question is is this drawing enough to show a bijection or do I need to do more?
Thank you for your thoughts.

I think your lines are not vertical, right?  With your construction, there are points on the semi-circle that do not have a corresponding point on the line.  But you are quite close.  You can 1) modify the construction so that every line from P through the semicircle hits the line (and still have every line from the line segment hit the semi-circle.  What does that tell you about the endpoints of each?) Or 2)find another construction that injects the semi-circle into the line, then argue from the Cantor–Bernstein–Schroeder theorem. 
