An exercise from "System of Coordinates" (by Gelfand, Glagoleva and Kirilov) asks me to "[t]ry to decide by yourself which sets of points are defined by these relations" and relations given are:
a. $|x| = |y|$;
b. $\frac{x}{|x|} = \frac{y}{|y|}$;
c. $|x| + x = |y| + y$;
d. $[x] = [y]$ ($[\gamma]$ is defined as giving whole part of $\gamma$);
e. $x - [x] = y - [y]$;
f. $x - [x] > y - [y]$.
What I'm having most trouble with is probably the notation as I don't think I understand the question(s) in the exercise properly. As an example a straight line, $x = y$ has been given, together with $x^2 - y^2 = 0$ which is also graphed as a straight line in example.
Case (a) could be reduced to $f(x) = |x|$ to be graphed, I think, but after that I'm at loss.
For example for case (b) I can graph $f(x) = \frac{x}{|x|}$ but what on earth am I to do with $\frac{x}{|x|} = \frac{y}{|y|}$? How can I graph something with two unknowns to a two-dimensional plane? It goes without a mention that I've got nowhere with cases c-f because I'm clearly not even getting the question.
The exercise is from page 18 of the book.