Definition:Real Interval/Notation/Conventional
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Definition
These are the notations usually seen for real intervals:
| \(\ds \left ({a, b}\right)\) | \(:=\) | \(\ds \set {x \in \R: a < x < b}\) | Open real interval | |||||||||||
| \(\ds \left [{a, b}\right)\) | \(:=\) | \(\ds \set {x \in \R: a \le x < b}\) | Half-open real interval | |||||||||||
| \(\ds \left ({a, b}\right]\) | \(:=\) | \(\ds \set {x \in \R: a < x \le b}\) | Half-open real interval | |||||||||||
| \(\ds \left [{a, b}\right]\) | \(:=\) | \(\ds \set {x \in \R: a \le x \le b}\) | Closed real interval |
but they can be confused with other usages for this notation.
In particular, there exists the danger of taking $\paren {a, b}$ to mean an ordered pair.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $7$: Common signs and symbols: interval