An open dot on a number line signifies that the number at that dot is not included in the set of values represented by the line. This is often used in conjunction with inequalities.
For example, if a number line shows an open dot at the number 3, it indicates that 3 is not part of the solution to the inequality. Instead, the line may represent values less than 3 (such as x < 3) or values greater than 3 (such as x > 3). The key point is that the value at the open dot is excluded from the defined range.
In contrast, a closed dot would indicate that the endpoint is included in the set, meaning the number itself is part of the solution. Understanding the distinction between open and closed dots helps in accurately interpreting mathematical expressions and inequalities.