{x | x ≤ 4.5} is another way to represent this solution set.
- A set is open if every point in is an interior point. A set is closed if it contains all of its boundary points.
What is open set example?
- An open subset of R is a subset E of R such that for every x in E there exists ϵ > 0 such that Bϵ(x) is contained in E.
- For example, the open interval (2,5) is an open set. Any open interval is an open set. Both R and the empty set are open.
What is an example of a closed set?
- The simplest example of a closed set is a closed interval of the real line [a,b].
- Any closed interval of the real numbers contains its boundary points by definition and is, therefore, a closed set.
- The closed interval [1,4] contains the limit points 1 and 4 so it is a closed set.
Then number-line shows a closed dot at 4.5. This shows that x is a number that is less than or equal to 4.5.
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