Understanding Closed Circles in Mathematics | Symbolizing Inclusive Endpoints and Precise Values

closed circle

In mathematics, a closed circle, also known as a solid dot or a filled-in dot, is a symbol used to represent a specific value on a number line or a coordinate plane

In mathematics, a closed circle, also known as a solid dot or a filled-in dot, is a symbol used to represent a specific value on a number line or a coordinate plane. It is often used in graphing to indicate that a particular value is included or equal to a certain point or number.

When graphing on a number line, a closed circle is used to represent an inclusive endpoint. This means that the value represented by the closed circle is included in the set of values being considered. For example, if we represent the set of integers greater than or equal to 3 on a number line, we would place a closed circle at the point labeled “3” to indicate that 3 is included in the set.

Similarly, on a coordinate plane, a closed circle is used to represent a specific point where the x and y coordinates have exact values. For example, if we had a point P with coordinates (2,4), we would plot this point on the coordinate plane using a closed circle at the location (2,4). This indicates that both the x and y coordinates of the point are exactly 2 and 4, respectively.

It is important to note that a closed circle is differentiated from an open circle, which is depicted as an empty dot. An open circle is used to represent an exclusive endpoint, meaning that the value represented by the open circle is not included in the set of values being considered. Open circles are commonly used when representing strict inequalities, such as x < 5 or y > -3.

Overall, a closed circle serves as a visual indicator to show that a specific value or point is included in a set or meets exact criteria in mathematical representations.

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