Closed intervals are closed

#closed sets#closed intervals#complement

Statement

Show that $[a,b]$ is closed in $\mathbb{R}$ .

Hint

Its complement $]-\infty,a[\cup]b,+\infty[$ is a union of open sets.

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Complement. $\mathbb{R}\setminus[a,b]=]-\infty,a[\cup]b,+\infty[$ , a union of open sets, hence open.

Conclusion. $[a,b]$ is closed.