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An open interval in the real numbers is an open set

**Prove** that an open interval in the real numbers is an open set and a closed interval is a closed set

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Anon User Points 0
Effectively: The closed set of the endpoints belonging to the set, which makes accurate border; therefore, the closed interval is a closed set. Example: \[3; 5\]; is not surrounded by elements belonging to the same set. The open-set "approaches the border through infinite possible values (with a difference as small as you want, always and when it is >0). Therefore, the open interval is an open set. Example: (3; 5); let's take the upper end, with a value of 4.999; it is located above with infinite values >4.999 and < 5. (note: this is not 4.999... newspaper).

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