Consider the following equivalence relation:
$ (x_1, x_2) \sim (y_1 ,y_2)$ iff $ x_1^2 + x_2^2 = y_1^2 + y_2^2 $
Now, find a bijection $ f: R^2/ \sim \rightarrow [0, \infty) $. From my understanding, the set of equivalence classes represents points on circles of any radius $ r \in R $. However, I am struggling with defining a bijective function, as I am failing injectivity on any attempt. Can someone provide some hint?