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In mathematics, nested brackets refer to brackets (or parentheses) that are placed within other brackets. This is used to indicate the order of operations when performing calculations. The expressions within the innermost brackets are evaluated first, followed by the next level of brackets, and so on, until all brackets have been resolved.
Here's an example to illustrate nested brackets:
2 * (3 + (4-1))
In this expression, the operations inside the innermost brackets are performed first:
- Evaluate the innermost brackets: ( 4 - 1 = 3 )
- Substitute back into the expression: (2 * (3 + 3)
- Evaluate the next level of brackets: (3+3 =6)
- Finally, perform the outermost operation:
2 * 6 = 12
Nested brackets help clarify the order in which operations should be performed, ensuring accurate results, especially in more complex mathematical expressions. The common types of brackets used are parentheses ( ), square brackets [ ], and curly brackets { }
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