Proving Sum of Open Balls B_r(α)+B_s(β) = B_{r+s}(α+β)

[yifli]

Homework Statement

Prove that the sum B_r(\alpha)+B_s(\beta) is exactly the ball B_{r+s}(\alpha+\beta)

Homework Equations

open ball B_r(\alpha) of radius r about the center \alpha is \left \{\epsilon: |\alpha-\epsilon|<r\right\}

The Attempt at a Solution

I have difficulty of proving B_{r+s}(\alpha+\beta) \subset B_r(\alpha)+B_s(\beta)
any hints?

Thanks

 

[gb7nash]

Are \alpha and \beta arbitrary complex numbers?

Edit: I read it again. I'll assume that alpha and beta are points in 3-space since you're talking about balls.