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

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Homework Statement


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

Homework Equations


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

The Attempt at a Solution


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

Thanks
 
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Are [tex]\alpha[/tex] and [tex]\beta[/tex] 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.