# Interval Notation

Interval Notation

A real interval is shown graphically and described in words, as a set, and in interval notation. (There is no interval notation for the empty set.) Here is a summary:

American | European | ||||

○ | open&closed | bounded | ∅ | — | — |

●—● | closed | " | {x|a≤x≤b} | [a,b] | [a,b] |

●—○ | half-open | " | {x|a≤x<b} | [a,b) | [a,b[ |

○—● | half-open | " | {x|a<x≤b} | (a,b] | ]a,b] |

○—○ | open | " | {x|a<x<b} | (a,b) | ]a,b[ |

●⟶ | closed | unbounded | {x|a≤x} | [a,∞) | [a,∞[ |

○⟶ | open | " | {x|a<x} | (a,∞) | ]a,∞[ |

⟵● | closed | " | {x|x≤b} | (-∞,b] | ]-∞,b] |

⟵○ | open | " | {x|x<b} | (-∞,b) | ]-∞,b[ |

⟷ | open&closed | " | | (-∞,∞) | ]-∞,∞[ |