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Interval notation is a shorthand method of writing down a range of values; typically, for real numbers. This notation consists of an opening and closing bracket, either a parenthesis or a square bracket, along with two numbers separated by a comma in between. The opening and closing brackets correspond to the lower and upper bounds of the range, respectively.

The key difference between parentheses and square brackets lies in the inclusion of the end-points: 1. Parentheses, '(' and ')', signify that the end-points of the interval are *not* included in the solution set. 2. Square brackets, '[' and ']', indicate that the end-points of the interval *are* included in the solution set.

Consider the following examples: Example 1: Set A consists of all real numbers between 2 and 5, excluding 2 and including 5. In this case, A = (2, 5], because 2 is not included (parenthesis) and 5 is included (square bracket). Example 2: Set B contains all real numbers greater than or equal to 7, but less than 10. Here, B = [7, 10) since 7 is included (square bracket) and 10 is not included (parenthesis). Example 3: Set C has all real numbers greater than -5 and less than 3, excluding both end-points. For this set, C = (-5, 3) because both end-points are not included (parentheses). So, when writing a solution set in interval notation, use square brackets to include the end-points and parentheses to exclude them.