what is a close circle in math mean
In mathematics, a "closed circle" is a term used to describe a point plotted on a number line or a graph. It indicates that the value represented by that point is included or "closed" within a particular set or interval. It is usually denoted by a solid dot.
To understand the concept of a closed circle, let's consider the notion of interval notation. In interval notation, closed intervals are represented using square brackets [ ]. For example, if we have an interval like [1, 5], it means that the interval includes all numbers from 1 to 5, including both endpoints. To depict this on a number line or a graph, we place a closed circle on the number 1 and another closed circle on the number 5, connecting them with a straight line.
Alternatively, an "open circle" is represented by parentheses ( ) and indicates that the corresponding value is excluded or "open" from the set or interval. For instance, if we have an interval like (1, 5), it means that the interval includes all numbers between 1 and 5 but excludes the endpoints. This is shown on a number line or a graph by placing open circles on the numbers 1 and 5, and drawing a line between them.
To summarize, a "closed circle" in math refers to a solid dot used to represent an inclusive endpoint in an interval or a set.