Assuming its endpoints are not equal, a closed interval of the real number line a has an infinite number of real numbers in it. Closed intervals of other ordered sets can have either a finite or an infinite number of elements.
I am not sure I answered your question because I am not exactly sure what you are asking. Could you be more specific? Are you talking about a closed interval of the real number line or closed interval of some other ordered set? By finite do you mean 'containing a finite number of elements' or do you mean 'bounded by a finite number'.
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Open interval does not include its end points while closed interval includes
Yes, if it is the closed interval. No, if it is the open interval.
Probability of an even must lie in the closed interval [0, 1].Probability of an even must lie in the closed interval [0, 1].Probability of an even must lie in the closed interval [0, 1].Probability of an even must lie in the closed interval [0, 1].
Because infinity is not a number.
Closed sets and open sets, or finite and infinite sets.