Question
Does [ and ( mean the same thing in math
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GPT-4o mini
In mathematics, the symbols "[" and "(" do not mean the same thing; they serve different purposes when denoting intervals.
- **Parentheses "(" and ")"** are used to indicate an **open interval**. An open interval does not include its endpoints. For example, the interval \((a, b)\) means all numbers \(x\) such that \(a < x < b\).
- **Brackets "[" and "]"** are used to denote a **closed interval**. A closed interval includes its endpoints. For example, the interval \([a, b]\) means all numbers \(x\) such that \(a \leq x \leq b\).
Additionally, you may encounter mixed intervals, such as \([a, b)\), which includes \(a\) but does not include \(b\), meaning \(a \leq x < b\).
In summary, the main difference is that brackets indicate inclusion of the endpoints, while parentheses indicate exclusion of the endpoints.
- **Parentheses "(" and ")"** are used to indicate an **open interval**. An open interval does not include its endpoints. For example, the interval \((a, b)\) means all numbers \(x\) such that \(a < x < b\).
- **Brackets "[" and "]"** are used to denote a **closed interval**. A closed interval includes its endpoints. For example, the interval \([a, b]\) means all numbers \(x\) such that \(a \leq x \leq b\).
Additionally, you may encounter mixed intervals, such as \([a, b)\), which includes \(a\) but does not include \(b\), meaning \(a \leq x < b\).
In summary, the main difference is that brackets indicate inclusion of the endpoints, while parentheses indicate exclusion of the endpoints.