Question

Let I ⊂ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≤ b and I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)

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Gene

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78 Answers

Answer:
I is nonempty real numbers bounded interval.
It's bounded so, there will two real numbers a,b such a ≤ x ≤ b for all x in I.
Since I is interval so ,
Either
I=[a,b] if a,b are also elements of I
Or,
I=(a,b] if b is also elements of I
Or,
I=[a,b) if a is also elements of I
Or,
I=(a,b) if a,b is not elements of I
Proved.

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