Equivalence relations problem #2 (alg)

[Pearce_09]

R = the real numbers

A = R x R; (x,y) \equiv (x_1,y_1) means that
x^2 + y^2 = x_1^2 + y_1^2; B= {x is in R | x>= 0 }

Find a well defined bijection sigma : A_\equiv -> B

like the last problem, I just can't seem to find the right way to solve this??

 

[matt grime]

hint 1 x^2+y^2 is a positive real number.

hint 2 What is an equivalence class under this relation, think geometrically.

hint 3 radius.

 

[fourier jr]

R = the real numbers

A = R x R; (x,y) \equiv (x_1,y_1) means that
x^2 + y^2 = x_1^2 + y_1^2; B= {x is in R | x>= 0 }

Find a well defined bijection sigma : A_\equiv -> B

like the last problem, I just can't seem to find the right way to solve this??

did you get it?

 

[Pearce_09]

ya i did thanks fourier