Square Bracket — Definition, Formula & Examples
Square brackets are the symbols [ and ] used in math to group expressions, denote closed intervals, or indicate special operations like the greatest integer function.
The square bracket symbols [ and ] serve as delimiters in mathematical notation. In interval notation, a square bracket indicates that the endpoint is included in the set (a closed boundary), in contrast to a parenthesis, which excludes the endpoint.
How It Works
Square brackets appear in several contexts. In interval notation, means every number from to , including both and . You can mix them with parentheses: includes 2 but not 5. Square brackets also group expressions just like parentheses, especially when parentheses are already in use, making nested expressions easier to read. For example, uses square brackets on the outside so you can clearly see the layers.
Worked Example
Problem: Simplify the expression .
Step 1: Start with the innermost parentheses.
Step 2: Add inside the square brackets.
Step 3: Multiply by the factor outside the square brackets.
Answer:
Why It Matters
Square brackets are essential in algebra and pre-calculus when writing solutions to inequalities as intervals. They also keep complex nested calculations readable, which matters whenever you solve multi-step problems or work with formulas in science and engineering.
Common Mistakes
Mistake: Confusing square brackets with parentheses in interval notation, writing when you mean .
Correction: A square bracket [ or ] means the endpoint IS included. A parenthesis ( or ) means it is NOT. Choose the symbol that matches whether the boundary value belongs to the set.