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Homework Statement
Suppose r and s are two positive real numbers. Let Dr and Ds be defined as in part 3 of Example 4.3.1. What is [tex]D_r \circ D_s[/tex]? Justify your answer with a proof. (Hint: In your proof, you may find it helpful to use the triangle inequality.)
Homework Equations
Example 4.3.1:
For each positive real number r, let Dr = [tex]\left\{(x,y)\in \mathbb{R} \times \mathbb{R} | ( |x - y| < r \right\}[/tex]. Then Dr is a relation on [tex]\mathbb{R}[/tex].
[tex]\circ[/tex] = composition
The Attempt at a Solution
I don't know what the composition of Dr and Ds would be, so I am not even close to being able to prove anything.
thanks
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