Question

What is another way to represent this solution set? {x | x < 4.5} {x | x ≤ 4.5} {x | x > 4.5} {x | x ≥ 4.5}

Answer 1

{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.

Learn more about closed set

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