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Open interval does not include its end points while closed interval includes

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Q: Differentiate a closed interval from an open interval?
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Will you find the number 89 in the interval 79-89?

Yes, if it is the closed interval. No, if it is the open interval.


Identify the interval -8 3 as open closed half open or unbounded?

Open


Is it possible to take the union of two open intervals and get a closed interval?

No.


Is it possible to take the union of infinitely many open intervals and get a closed interval?

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An open interval, usually written as (2, 4) is any number between 2 and 4 but excluding the two end points. Another way of writing it is {x : 2 < x < 4}. A closed interval includes both end points and a semi-open or semi-closed includes one but not both.


The interval notation for the interval of real numbers?

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Define intervals on the number scale?

An interval on the number scale is a set of numbers between two end-point. Thus the closed interval [a, b] comprises all number between a and b as well as the two end points. An interval is open if neither end point is included, and semi-open (or semi-closed) if one end in included and the other is not.


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Why in rolles theorem closed interval is used for contuinity and open interval is used for differentiability?

It requires that f(a)=f(b) where a and b are beginning and ending points. Also, it says there is a c between a and such that f'(c)=0. If f were not differentiable on the open interval, the statement f'(c)=0 would be invalid.