I'm struggling to solve the problem stated above. To help clarify the question I let a = 1, b = 2, c = 3,and d = 4. If that were the case then the interval I am interested is [b, c]. What does it mean to express that as the difference of two intervals?
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You're right, $[a,c] \cap [b,d] = [b,c]$. To express $[b,c]$ as a difference of intervals, you need intervals $I$ and $J$ such that $[b,c] = I \setminus J$. For example, you can write $[b,c] = [b,d]\setminus(c,d)$, since $(c,d)$ is contained in $[b,d]$ and every element of $[b,c]$ is an element of $[b,d]$ that is not in $(c,d)$.
kobe
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Why would you want to express it as the difference of two intervals? We have some options here, but none of them say anything worthwhile. For example, [b,c] = [a,c] - [a,b).
Chris
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