intervals of subset
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Intervals: An interval is a subset I of R∗ satisfying the following requirement: Whenever x < y < z and x,z ∈ I then y ∈ I. Obvious examples are the sets we have been taught to consider intervals: (a,b) = {x : a < x < b}, [a,b] = {x : a ≤ x ≤ b}, (a,b] = {x : a < x ≤ b}, [a,b) = {x : a ≤ x < b}.
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Answer:
Intervals: An interval is a subset I of R∗ satisfying the following requirement: Whenever x < y < z and x,z ∈ I then y ∈ I. Obvious examples are the sets we have been taught to consider intervals: (a,b) = {x : a < x < b}, [a,b] = {x : a ≤ x ≤ b}, (a,b] = {x : a < x ≤ b}, [a,b) = {x : a ≤ x < b}.
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